Two Parameter Asymptotic Spectra

The two parameter eigenvalue problem in Hilbert space is discussed for selfadjoint operators T. with discrete spectrum and bounded symmetric V_jk satisfying “uniform right definiteness”. Then there are countably many eigenvalues in ?². Results are given relating the set of limit points of ) to a set defined entirely by the V_jk.     

Variational method for precise asymptotic formulas for nonlinear eigenvalue problems

We consider the nonlinear eigenvalue problem motivated by the perturbed elliptic sine-Gordon equation where p >1 is a constant and λ ∈ R is an eigenvalue parameter. Our aim is to clarify the asymptotic relationship between L ^p+1-norm, L ^∞-norm of the solutions and λ when these norms are large. To this end, we consider an associated variational problem with this equation on a manifold new parameter), and obtain a solution pair . We establish the precise asymptotic formulas for .     

Trace series on

Let K be a number field which contains the absolute Galois group of K. Let be the completion of relative to the spectral norm . A trace series and a trace function are associated to an element . A measure preserving function H:G{inK}→[0,1] is constructed and a Fourier type theory is considered for elements of .     

A galois theory for the banach algebra of continuous symmetric functions on absolute galois groups

In this paper we extend the techniques and the basic results of the classical Galois theory of the fields extension is an algebraic closure of Q, to the algebras extension ? ? ?_sym(G), where this last is the ?— algebra of all the continuous symmetric functions ? defined on the absolute Galois group with values in ?.     

On the best convergence of trigonometric integrals

ОсНОВНОИ РЕжУльтАт Ё тОИ стАтьИ жАклУЧАЕт сь В слЕДУУЩЕМ. ЕслИ с ФИксИРОВАННыМr=2, 3,..., тО Дль тОгО, ЧтОБы ИМЕлО М ЕстО (*) гДЕ ДОстАтОЧНО ВыпОлНЕН ИЕ слЕДУУЩИх УслОВИИ: 1) ЕслИ $$1< \frac{{n_\nu + 1}}{{n_\nu }} = g_\nu \in N, \nu = 0,1,$$ тО Дль кАжДОгОΝ=0,1,... ИМЕ Ет МЕстО (**) 2) ЕслИ тО (***) $$n_{\nu + 1} \geqslant (2r - 1)n_\nu , \nu = 0,1,...$$ . ЕслИ И тО УслОВИь (**), (***) ьВльУтсь тАкжЕ НЕОБхОДИМыМИ Д ль (*).     

The Approximation of The Continuous Functions by Means of Some Linear Positive Operators

In this paper we give positive answers to some problems posed by H.Gonska, respectively A.Lupa?. We show here that there exist positive linear operators H _n : C[0, 1] → π_n satisfying      

On inductive limits of measure spaces

We introduce a category of (topological) measure spaces in which inductive limitis exist and where the Banach spaces and (1≤p≤+∞) are isometric for arbitrary inductive systems of (topological) measure spaces.     

Polylogarithms in the Theory of Univalent Functions

Let a, b > ?1, p and q be non-zero real numbers such that p + q ≥ 1. In this paper, we study the geometric mapping properties of the (normalized) generalized polylogarithm defined in the unit disc      

Anisotropic inverse harmonic mean curvature flow

We study the evolution of convex hypersurfaces H（., t） with initial H（., 0） = 0H0 at a rate equal to H - f along its outer normal, where H is the inverse of harmonic mean curvature of H（., t）, H0 is a smooth, closed, and uniformly convex hypersurface. We find a θ^＊ 〉 0 and a sufficient condition about the anisotropic function f, such that if θ 〉 θ^＊, then H（.,t） remains uniformly convex and expands to infinity as t →∞ and its scaling, H（-, t）e^-nt, converges to a sphere. In addition, the convergence result is generalized to the fully nonlinear case in which the evolution rate is log H - log f instead of H - f.     

On minimal non- -groups

A finite group G is called an J N J-group if every proper subgroup H of G is either subnormal in G or self-normalizing. We determinate the structure of non-J N J-groups in which all proper subgroups are J N J- groups.     

Lelong numbers of positive plurisubharmonic currents

A (k,k)-current T on an open subset of C^N is plurisubharmonic if is positive. Positive plurisubharmonic currents admit Lelong numbers; we prove here that they are independent on the coordinates system. Moreover, if Y is an analytic subset of pure dimension, then the Lelong numbers of T on Y are given by a non negative weakly plurisubharmonic function.     

Wavelet transform and radon transform on the quaternion Heisenberg group

Let Q be the quaternion Heisenberg group,and let P be the affine automorphism group of Q.We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary representations of P on L2(Q).A class of radial wavelets is constructed.The inverse wavelet transform is simplified by using radial wavelets.Then we investigate the Radon transform on Q.A Semyanistyi–Lizorkin space is introduced,on which the Radon transform is a bijection.We deal with the Radon transform on Q both by the Euclidean Fourier transform and the group Fourier transform.These two treatments are essentially equivalent.We also give an inversion formula by using wavelets,which does not require the smoothness of functions if the wavelet is smooth.In addition,we obtain an inversion formula of the Radon transform associated with the sub-Laplacian on Q.     

Ein zerlegungssatz für P(ϰ)

We shall prove the following partition theorems:

1. For every setS and for each cardinal ? ≥ ω, |S| ≥ ? there exists a partitionT: [S]^? → 2^? such that for every pairwise disjoint familie and everyα < 2^? there exists a set
2. Suppose ? ≥ ω, 2 ^{andS an arbitrary set, 2|S| ≤ (2?)+ω Then there exists a partitionT: P(S) → 2? such that for every pairwise disjoint family and everyα < 2? there exists a set Both theorems will give partial answers to an Erd?s problem.}

     

On the class of groups with pronormal hall π-subgroups

Given a set π of prime numbers, we define the class of all finite groups in which Hall π-subgroups exist and are pronormal by analogy with the Hall classes , , and . We study whether is closed under the main class-theoretic closure operations. In particular, we establish that is a saturated formation.     

Super -operators of Jordan superalgebras and super Jordan Yang-Baxter equations

Abstract In this paper, the super t~-operators of Jordan superalgebras are introduced and the solutions of super Jordan Yang-Baxter equation are discussed by super б-operators. Then pre-Jordan superalgebras are studied as the algebraic structure behind the super б-operators. Moreover, the relations among Jordan superalgebras, pre-Jordan superalgebras, and dendriform superalgebras are established. Keywords Super б-operator, dendriform superalgebra, pre-Jordan superalgebra     

Topological spaces compact with respect to a set of filters

If is a family of filters over some set I, a topological space X is sequencewise -compact if for every I-indexed sequence of elements of X there is such that the sequence has an F-limit point. Countable compactness, sequential compactness, initial κ-compactness, [λ; µ]-compactness, the Menger and Rothberger properties can all be expressed in terms of sequencewise -compactness for appropriate choices of . We show that sequencewise -compactness is preserved under taking products if and only if there is a filter such that sequencewise -compactness is equivalent to F-compactness. If this is the case, and there exists a sequencewise -compact T ₁ topological space with more than one point, then F is necessarily an ultrafilter. The particular case of sequential compactness is analyzed in detail.     

Characterization of compact quantum group

Given a C^＊-algebra A and a comultiplication Ф on A, we show that the pair （A, Ф） is a compact quantum group if and only if the associated multiplier Hopf ^＊-algebra （A, ФA） is a compact Hopf ^＊-algebra.     

On additivity of mappings on measurable functions

We prove the additivity of regular l-additive mappings T: → [0,+∞] of a hereditary cone in the space of measurable functions on a measure space. Some examples are constructed of non-d-additive l-additive mappings T. The monotonicity of l-additive mappings T: → [0,+∞] is established. The examples are constructed of nonmonotone d-additive mappings T. Let (S, +) be a commutative cancellation semigroup. Given a mapping T: → S, we prove the equivalence of additivity and l-additivity. It is shown that a strongly regular 2-homogeneous l-subadditive mapping T is subadditive. All results are new even in case = L _∞ ⁺ .     

Isometric approximation property of unbounded sets

We give a necessary and sufficient quantitative geometric condition for an unbounded set A ? Rⁿ to have the following property with a given c > 0: For every ε ≥ 0 and for every map f: A → Rⁿ such that , there is an isometry T: A → Rⁿ such that ¦Tx?fx¦ ≤ cε for all x ∈ A.