Weights for the steinberg triality groups3 D 4(q)

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Green’s relations and regularity for semigroups of transformations that preserve order and a double direction equivalence

Let T _X be the full transformation semigroup on a set X,

Riemannian metrics on Teichmüller space

On each compact Riemann surface Σ of genusp≥1, we have the Bergman metric obtained by pulling back the flat metric on its Jacobian via the Albanese map. Taking theL ²-product of holomorphic quadratic differentials w.r.t. this metric induces a Riemannian metric on the Teichmüller spaceT _p that is invariant under the action of the modular group. We investigate geometric properties of this metric as an alternative to the usually employed Weil-Petersson metric. This article was processed by the author using the L^AT_EX style filecljour1 from Springer-Verlag.     

A Note on Classes of BANACH Spaces Related to Stable Measures

The problem under consideration is the following: Let S: E′ → L_q, T: E′ → L_p, 0 < q ≦ 2, 0 < p ≦ 2, be operators, ‖Sa‖ ≦ ‖Ta‖, such that, T generates a stable measure on E, i.e., exp (-‖Ta‖ ^p), a ? E′, is the characteristic function of a RADON measure on E. Does this imply, that exp (-‖Sa‖ q), a ? E′, is the characteristic function of a RADON measure, too? In general this is not true provided q or p less than 2. A BANACH space is said to be of (q,p)-cotype if the answer to the above question is “yes”. We establish several properties of this classification and obtain as an application the well-known classes due to MOUCHTARI, TIEN, WERON and MANDREKAR, WERON, Finally we apply our results to so-called S-spaces.     

Tame and galois extensions with respect to hopf orders

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Green’s relations and regularity for semigroups of transformations that preserve double direction equivalence

Let T _X denote the full transformation semigroup on a set X. For an equivalence E on X, let $T_{E^*}(X)=\{\alpha\in T_X:\forall x,y\in X,(x,y)\in E\Leftrightarrow(x\alpha,y\alpha)\in E\}.$ Then $T_{E^{*}}(X)Let T _X denote the full transformation semigroup on a set X. For an equivalence E on X, let

TE*(X)={a ? TX:"x,y ? X,(x,y) ? E?(xa,ya) ? E}.T_{E^*}(X)=\{\alpha\in T_X:\forall x,y\in X,(x,y)\in E\Leftrightarrow(x\alpha,y\alpha)\in E\}.      7. Metrica hermitiana ellittica in uno spazio proiettivo quaternionale      Maria Tallini Scafati 《Annali di Matematica Pura ed Applicata》1962,60(1):203-233 Riassunto Si definisce e si studia una nozione di distanza nello spazio proiettivo q aternionaleT n Q , la quale si riduce nell'infinitesimo alla meirica riemanniana del modello metrico reale diT n Q assegnato daMartinelli, e subordina le nozioni di distanza diCayley-Klein e diFubini-Study negli spazi proiettivi reale e complessoT n R ,T n C subordinati aT n Q . A M. Enrico Bompiani nel suo giubileo scientifico Lavoro eseguito nell'ambito del Gruppo di ricerca n. 37 del C. N. R.      8. Integral Transforms of Functionals in L 2(C a,b [0,T])      Seung Jun Chang  Hyun Soo Chung  David Skoug 《Journal of Fourier Analysis and Applications》2009,15(4):441-462 In this paper we use generalized Fourier-Hermite functionals to obtain a complete orthonormal set in L 2(C a,b [0,T]) where C a,b [0,T] is a very general function space. We then proceed to give a necessary and sufficient condition that a functional F in L 2(C a,b [0,T]) has an integral transform ℱ γ,β F also belonging to L 2(C a,b [0,T]).      9. Torus quotients of homogeneous spaces — II      S. Senthamarai Kannan 《Proceedings Mathematical Sciences》1999,109(1):23-39 We classify the homogeneous spacesX for which there is aT linearised ample line bundleL onX such thatX T ss(L)=XT s(L).      10. Periodic equivariant realK-theories have rational Tate theory      Lisbeth Fajstrup 《manuscripta mathematica》1996,91(1):211-221 Summary We study a generalized equivariantK-theory introduced by M. Karoubi. We prove, that it is anRO (G, U)-graded cohomology-theory and that the associated Tate spectrum is rational whenG is finite. This implies that for finite groups, the Atiyah-Segal Real equivariantK-theories have rational Tate theory. This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag      11. A normal form for curves in Grassmannians      Jens Piontkowski 《manuscripta mathematica》1996,89(1):79-85 The purpose of this paper is to give an elementary proof of Griffiths' and Harris' normal form lemma [4, p.385]. The author thanks Gerd Fischer for his encouragement and support This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag.      12. Gorenstein differential graded algebras      Anders?FrankildEmail author  Peter?J?rgensen 《Israel Journal of Mathematics》2003,135(1):327-353 We propose a definition of Gorenstein Differential Graded Algebra. In order to give examples, we introduce the technical notion of Gorenstein morphism. This enables us to prove the following: Theorem:Let A be a noetherian local commutative ring, let L be a bounded complex of finitely generated projective A-modules which is not homotopy equivalent to zero, and let ɛ=Hom A (L, L)be the endomorphism Differential Graded Algebra of L. Then ɛ is a Gorenstein Differential Graded Algebra if and only if A is a Gorenstein ring. Theorem:Let A be a noetherian local commutative ring with a sequence of elements a=(a 1,…,a n )in the maximal ideal, and let K(a)be the Koszul complex of a.Then K(a)is a Gorenstein Differential Graded Algebra if and only if A is a Gorenstein ring. Theorem:Let A be a noetherian local commutative ring containing a field k, and let X be a simply connected topological space with dim k H*(X;k)<∞,which has poincaré duality over k. Let C*(X;A)be the singular cochain Differential Graded Algebra of X with coefficients in A. Then C*(X; A)is a Gorenstein Differential Graded Algebra if and only if A is a Gorenstein ring. The second of these theorems is a generalization of a result by Avramov and Golod from [4].      13. Trace formulae forS 1 invariant green’s operators onS 2      Martin Engman 《manuscripta mathematica》1997,93(1):357-368 Summary We study the spectrum of the Laplacian acting on 1-forms for a surface of revolution diffeomorphic toS 2 and obtain, for theS 1 invariant spectrum, a trace formula for the eigenvalues of its Green’s operator. The trace formula is used to “hear” negative curvature for some metrics and to prove the existence of metrics onS 2 with rather unusual spectral characteristics. This article was processed by the author using the LATEX style file from Springer-Verlag.      14. Optimal interpolation in spaces of Lorentz-Zygmund type      Evgeniy Pustylnik 《Journal d'Analyse Mathématique》1999,79(1):113-157 The Lorentz-Zygmund spaces, introduced by C. Bennett and K. Rudnick in [BR], are generalized by taking the exterior norm in arbitrary rearrangement invariant spaceE instead of onlyL r-spaces. On the spacesL p,α,E thus obtained, we study all operatorsT of two weak types (a, b) and (p, q) with 1≤a<p≤∞, 1≤b<q≤∞, and prove thatT:L p,α,E→L q,α−1,E. Moreover, for any set of parametersp, q, α, E, we construct the smallest possible spaceB q,α,E such thatT:L p,α,E→B q,α,E and the largest possible spaceA p,α,E such thatT:A p,α,E→L q,α−1,E. For spaces of all three types, we find their fundamental functions and Boyd indices, state various embeddings, equivalences and other properties. The research was supported by the Center of Scientific Absorption of the Ministry of Absorption of the State of Israel.      15. Ambiguous loci of the metric projection onto compact starshaped sets in a Banach space   总被引：1，自引：0，他引：1   F. S. De Blasi  P. S. Kenderov  J. Myjak 《Monatshefte für Mathematik》1995,119(1-2):23-36 LetE be a real Banach space andL(E) the family of all nonempty compact starshaped subsets ofE. Under the Hausdorff distance,L(E) is a complete metric space. The elements of the complement of a first Baire category subset ofL(E) are called typical elements ofL(E). ForXL(E) we denote by the metrical projection ontoX, i.e. the mapping which associates to eachaE the set of all points inX closest toa. In this note we prove that, ifE is strictly convex and separable with dimE2, then for a typicalXL(E) the map is not single valued at a dense set of points. Moreover, we show that a typical element ofL(E) has kernel consisting of one point and set of directions dense in the unit sphere ofE.      16. The spectrum of the averaging operator for a finite homogeneous graph      A. M. Nikitin 《Journal of Mathematical Sciences》1996,80(3):1818-1828 We give an estimate for the spectrum of the averaging operator T1(Γ, 1) over the radius 1 for the finite (q+1)-homogeneous quotient graph Γ/X, where X is an infinite (q+1)-homogeneous tree associated with the free group G over a finite set of generators S={x1 ..., xp} (2p=q+1), and Γ, a subgroup of finite index in G. T1(Γ, 1) is defined on the subspace L2(Γ/G, 1) ⊖ Eex, where Eex is the subspace of eigenfunctions of T1(Γ, 1) with eigenvalue λ such that |λ|=q+1. We present a construction of some finite homogeneous graphs such that the spectrum of their adjacency matrices can be calculated explicitly. Bibliography: 11 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 205, 1993, pp. 92–109. Translated by A. M. Nikitin.      17. Special orthogonal splittings of<Emphasis Type="Italic">L</Emphasis><Stack><Subscript>1</Subscript><Superscript>2<Emphasis Type="Italic">k</Emphasis></Superscript></Stack>      Gideon?SchechtmanEmail author 《Israel Journal of Mathematics》2004,139(1):337-347 We show that for each positive integerk there is ak×k matrixB with ±1 entries such that puttingE to be the span of the rows of thek×2k matrix [√kI k,B], thenE,E ⊥ is a Kashin splitting: TheL 1 2k and theL 2 2k are universally equivalent on bothE andE ⊥. Moreover, the probability that a random ±1 matrix satisfies the above is exponentially close to 1. Supported by the Israel Science Foundation.      18. Basic Results of Gabor Frame on Local Fields          下载免费PDF全文 Dengfeng LI  Huikun JIANG 《数学年刊B辑(英文版)》2007,28(2):165-176 Basic facts for Gabor frame {Eu(m)bTu(n)ag}m,n∈p on local field are investigated. Accurately, that the canonical dual of frame {Eu(m)bTu(n)ag}m,n∈p also has the Gabor structure is showed; that the product ab decides whether it is possible for {Eu(m)bTu(n)ag}m,n∈p to be a frame for L2(K) is discussed; some necessary conditions and two sufficient conditions of Gabor frame for L2(K) are established. An example is finally given.      19. Note on the Casson-Gordon invariant of a satellite knot      Hamid Abchir 《manuscripta mathematica》1996,90(1):511-519 In this paper we establish a relation between an appropriate version of the Casson-Gordon invariant of a satellite knot and those of its orbit and companion. We note that in some cases the contribution from, the companion falls. This gives a way to construct algebraically but not smoothly slice knots. This article was processed by the author using theLaTEX style filecljouri from Springer-Verlag.      20. Differentiable and analytic families of continuous martingales in manifolds with connection      Marc Arnaudon 《Probability Theory and Related Fields》1997,108(2):219-257 Summary.  We prove that the derivative of a differentiable family X t (a) of continuous martingales in a manifold M is a martingale in the tangent space for the complete lift of the connection in M, provided that the derivative is bicontinuous in t and a. We consider a filtered probability space (Ω,(ℱ t )0≤ t ≤1, ℙ) such that all the real martingales have a continuous version, and a manifold M endowed with an analytic connection and such that the complexification of M has strong convex geometry. We prove that, given an analytic family a↦L(a) of random variable with values in M and such that L(0)≡x 0∈M, there exists an analytic family a↦X(a) of continuous martingales such that X 1(a)=L(a). For this, we investigate the convexity of the tangent spaces T ( n ) M, and we prove that any continuous martingale in any manifold can be uniformly approximated by a discrete martingale up to a stopping time T such that ℙ(T<1) is arbitrarily small. We use this construction of families of martingales in complex analytic manifolds to prove that every ℱ1-measurable random variable with values in a compact convex set V with convex geometry in a manifold with a C 1 connection is reachable by a V-valued martingale. Received: 14 March 1996/In revised form: 12 November 1996

Metrica hermitiana ellittica in uno spazio proiettivo quaternionale

Riassunto Si definisce e si studia una nozione di distanza nello spazio proiettivo q aternionaleT _n ^Q , la quale si riduce nell'infinitesimo alla meirica riemanniana del modello metrico reale diT _n ^Q assegnato daMartinelli, e subordina le nozioni di distanza diCayley-Klein e diFubini-Study negli spazi proiettivi reale e complessoT _n ^R ,T _n ^C subordinati aT _n ^Q . A M. Enrico Bompiani nel suo giubileo scientifico Lavoro eseguito nell'ambito del Gruppo di ricerca n. 37 del C. N. R.     

Integral Transforms of Functionals in L 2(C a,b [0,T])

In this paper we use generalized Fourier-Hermite functionals to obtain a complete orthonormal set in L ²(C _a,b [0,T]) where C _a,b [0,T] is a very general function space. We then proceed to give a necessary and sufficient condition that a functional F in L ²(C _a,b [0,T]) has an integral transform ℱ _γ,β F also belonging to L ²(C _a,b [0,T]).     

Torus quotients of homogeneous spaces — II

We classify the homogeneous spacesX for which there is aT linearised ample line bundleL onX such thatX _T ^ss(L)=X_T ^s(L).     

Periodic equivariant realK-theories have rational Tate theory

Summary We study a generalized equivariantK-theory introduced by M. Karoubi. We prove, that it is anRO (G, U)-graded cohomology-theory and that the associated Tate spectrum is rational whenG is finite. This implies that for finite groups, the Atiyah-Segal Real equivariantK-theories have rational Tate theory. This article was processed by the author using the L^AT_EX style filecljour1 from Springer-Verlag     

A normal form for curves in Grassmannians

The purpose of this paper is to give an elementary proof of Griffiths' and Harris' normal form lemma [4, p.385]. The author thanks Gerd Fischer for his encouragement and support This article was processed by the author using the L^AT_EX style filecljour1 from Springer-Verlag.     

Gorenstein differential graded algebras

We propose a definition of Gorenstein Differential Graded Algebra. In order to give examples, we introduce the technical notion of Gorenstein morphism. This enables us to prove the following: Theorem:Let A be a noetherian local commutative ring, let L be a bounded complex of finitely generated projective A-modules which is not homotopy equivalent to zero, and let ɛ=Hom _A (L, L)be the endomorphism Differential Graded Algebra of L. Then ɛ is a Gorenstein Differential Graded Algebra if and only if A is a Gorenstein ring. Theorem:Let A be a noetherian local commutative ring with a sequence of elements a=(a ₁,…,a _n )in the maximal ideal, and let K(a)be the Koszul complex of a.Then K(a)is a Gorenstein Differential Graded Algebra if and only if A is a Gorenstein ring. Theorem:Let A be a noetherian local commutative ring containing a field k, and let X be a simply connected topological space with dim _k H*(X;k)<∞,which has poincaré duality over k. Let C*(X;A)be the singular cochain Differential Graded Algebra of X with coefficients in A. Then C*(X; A)is a Gorenstein Differential Graded Algebra if and only if A is a Gorenstein ring. The second of these theorems is a generalization of a result by Avramov and Golod from [4].     

Trace formulae forS 1 invariant green’s operators onS 2

Summary We study the spectrum of the Laplacian acting on 1-forms for a surface of revolution diffeomorphic toS ² and obtain, for theS ¹ invariant spectrum, a trace formula for the eigenvalues of its Green’s operator. The trace formula is used to “hear” negative curvature for some metrics and to prove the existence of metrics onS ² with rather unusual spectral characteristics. This article was processed by the author using the L^AT_EX style file from Springer-Verlag.     

Optimal interpolation in spaces of Lorentz-Zygmund type

The Lorentz-Zygmund spaces, introduced by C. Bennett and K. Rudnick in [BR], are generalized by taking the exterior norm in arbitrary rearrangement invariant spaceE instead of onlyL _r-spaces. On the spacesL _p,α,E thus obtained, we study all operatorsT of two weak types (a, b) and (p, q) with 1≤a<p≤∞, 1≤b<q≤∞, and prove thatT:L _p,α,E→L _q,α−1,E. Moreover, for any set of parametersp, q, α, E, we construct the smallest possible spaceB _q,α,E such thatT:L _p,α,E→B _q,α,E and the largest possible spaceA _p,α,E such thatT:A _p,α,E→L _q,α−1,E. For spaces of all three types, we find their fundamental functions and Boyd indices, state various embeddings, equivalences and other properties. The research was supported by the Center of Scientific Absorption of the Ministry of Absorption of the State of Israel.     

Ambiguous loci of the metric projection onto compact starshaped sets in a Banach space

LetE be a real Banach space andL(E) the family of all nonempty compact starshaped subsets ofE. Under the Hausdorff distance,L(E) is a complete metric space. The elements of the complement of a first Baire category subset ofL(E) are called typical elements ofL(E). ForXL(E) we denote by the metrical projection ontoX, i.e. the mapping which associates to eachaE the set of all points inX closest toa. In this note we prove that, ifE is strictly convex and separable with dimE2, then for a typicalXL(E) the map is not single valued at a dense set of points. Moreover, we show that a typical element ofL(E) has kernel consisting of one point and set of directions dense in the unit sphere ofE.     

The spectrum of the averaging operator for a finite homogeneous graph

We give an estimate for the spectrum of the averaging operator T₁(Γ, 1) over the radius 1 for the finite (q+1)-homogeneous quotient graph Γ/X, where X is an infinite (q+1)-homogeneous tree associated with the free group G over a finite set of generators S={x₁ ..., x_p} (2p=q+1), and Γ, a subgroup of finite index in G. T₁(Γ, 1) is defined on the subspace L²(Γ/G, 1) ⊖ E_ex, where E_ex is the subspace of eigenfunctions of T₁(Γ, 1) with eigenvalue λ such that |λ|=q+1. We present a construction of some finite homogeneous graphs such that the spectrum of their adjacency matrices can be calculated explicitly. Bibliography: 11 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 205, 1993, pp. 92–109. Translated by A. M. Nikitin.     

Special orthogonal splittings of<Emphasis Type="Italic">L</Emphasis><Stack><Subscript>1</Subscript><Superscript>2<Emphasis Type="Italic">k</Emphasis></Superscript></Stack>

We show that for each positive integerk there is ak×k matrixB with ±1 entries such that puttingE to be the span of the rows of thek×2k matrix [√kI _k,B], thenE,E ^⊥ is a Kashin splitting: TheL ₁ ^2k and theL ₂ ^2k are universally equivalent on bothE andE ^⊥. Moreover, the probability that a random ±1 matrix satisfies the above is exponentially close to 1. Supported by the Israel Science Foundation.     

Basic Results of Gabor Frame on Local Fields

Basic facts for Gabor frame {Eu(m)bTu(n)ag}m,n∈p on local field are investigated. Accurately, that the canonical dual of frame {Eu(m)bTu(n)ag}m,n∈p also has the Gabor structure is showed; that the product ab decides whether it is possible for {Eu(m)bTu(n)ag}m,n∈p to be a frame for L2(K) is discussed; some necessary conditions and two sufficient conditions of Gabor frame for L2(K) are established. An example is finally given.     

Note on the Casson-Gordon invariant of a satellite knot

In this paper we establish a relation between an appropriate version of the Casson-Gordon invariant of a satellite knot and those of its orbit and companion. We note that in some cases the contribution from, the companion falls. This gives a way to construct algebraically but not smoothly slice knots. This article was processed by the author using theLaT_EX style filecljouri from Springer-Verlag.     

Differentiable and analytic families of continuous martingales in manifolds with connection

Summary.  We prove that the derivative of a differentiable family X _t (a) of continuous martingales in a manifold M is a martingale in the tangent space for the complete lift of the connection in M, provided that the derivative is bicontinuous in t and a. We consider a filtered probability space (Ω,(ℱ _t )_{0≤ t ≤1}, ℙ) such that all the real martingales have a continuous version, and a manifold M endowed with an analytic connection and such that the complexification of M has strong convex geometry. We prove that, given an analytic family a↦L(a) of random variable with values in M and such that L(0)≡x ₀∈M, there exists an analytic family a↦X(a) of continuous martingales such that X ₁(a)=L(a). For this, we investigate the convexity of the tangent spaces T ^{( n )} M, and we prove that any continuous martingale in any manifold can be uniformly approximated by a discrete martingale up to a stopping time T such that ℙ(T<1) is arbitrarily small. We use this construction of families of martingales in complex analytic manifolds to prove that every ℱ₁-measurable random variable with values in a compact convex set V with convex geometry in a manifold with a C ¹ connection is reachable by a V-valued martingale. Received: 14 March 1996/In revised form: 12 November 1996