共查询到20条相似文献,搜索用时 15 毫秒
1.
Let G be the group of points of a split reductive algebraic group G over a local field k and let X = G / U where U is the group of k-points of a maximal unipotent subgroup of G. In this paper we construct a certain canonical G-invariant space (called the Schwartz space of X) of functions on X, which is an extension of the space of smooth compactly supported functions on X. We show that the space of all elements of , which are invariant under the Iwahori subgroup I of G, coincides with the space generated by the elements of the so called periodic Lusztig basis, introduced recently by G. Lusztig
(cf. [10] and [11]). We also give an interpretation of this space in terms of a certain equivariant K-group (this was also
done by G. Lusztig — cf. [12]). Finally we present a global analogue of , which allows us to give a somewhat non-traditional treatment of the theory of the principal Eisenstein series. 相似文献
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In this paper we give a simpler proof of the L
p
-Schwartz space isomorphism (0 < p ≤ 2) under the Fourier transform for the class of functions of left δ-type on a Riemannian symmetric space of rank one. Our treatment rests on Anker’s [2] proof of the corresponding result in
the case of left K-invariant functions on X. Thus we give a proof which relies only on the Paley-Wiener theorem. 相似文献
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Soon-Yeong Chung Dohan Kim Sungjin Lee 《Proceedings of the American Mathematical Society》1997,125(11):3229-3234
We give an elementary proof of the equivalence of the original definition of Schwartz and our characterization for the Schwartz space . The new proof is based on the Landau inequality concerning the estimates of derivatives. Applying the same method, as an application, we give a better symmetric characterization of the Beurling-Björck space of test functions for tempered ultradistributions with respect to Fourier transform without conditions on derivatives.
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Yiannis Sakellaridis 《Selecta Mathematica, New Series》2016,22(4):2401-2490
Schwartz functions, or measures, are defined on any smooth semi-algebraic (“Nash”) manifold, and are known to form a cosheaf for the semi-algebraic restricted topology. We extend this definition to smooth semi-algebraic stacks, which are defined as geometric stacks in the category of Nash manifolds. Moreover, when those are obtained from algebraic quotient stacks of the form X/G, with X a smooth affine variety and G a reductive group defined over a number field k, we define, whenever possible, an “evaluation map” at each semisimple k-point of the stack, without using truncation methods. This corresponds to a regularization of the sum of those orbital integrals whose semisimple part corresponds to the chosen k-point. These evaluation maps produce, in principle, a distribution which generalizes the Arthur–Selberg trace formula and Jacquet’s relative trace formula, although the former, and many instances of the latter, cannot actually be defined by the purely geometric methods of this paper. In any case, the stack-theoretic point of view provides an explanation for the pure inner forms that appear in many versions of the Langlands, and relative Langlands, conjectures. 相似文献
8.
The existence of an infinite number of periodic solutions of a quasilinear wave equation with variable coefficients, with Dirichlet and Neumann boundary conditions on the closed interval and with time-periodic right-hand side is proved. The nonlinear summand has a power-law growth. 相似文献
9.
S. Z. Levendorskii 《Acta Appl Math》1986,7(2):137-197
In this paper we develop a general method for investigating the spectral asymptotics for various differential and pseudo-differential operators and their boundary value problems, and consider many of the problems posed when this method is applied to mathematical physics and mechanics. Among these problems are the Schrödinger operator with growing, decreasing and degenerating potential, the Dirac operator with decreasing potential, the quasi-classical spectral asymptotics for Schrödinger and Dirac operators, the linearized Navier-Stokes equation, the Maxwell system, the system of reactor kinetics, the eigenfrequency problems of shell theory, and so on. The method allows us to compute the principal term of the spectral asymptotics (and, in the case of Douglis-Nirenberg elliptic operators, also their following terms) with the remainder estimate close to that for the sharp remainder. 相似文献
10.
Jaeyoung Chung Soon-Yeong Chung 《Journal of Mathematical Analysis and Applications》2004,295(1):107-114
We reformulate the stability theorem of D.H. Hyers in the Schwartz tempered distributions and prove that every ?-additive tempered distribution can be approximated by a linear function. We also consider the superstability of the Cauchy equation f(x+y)=f(x)f(y). 相似文献
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In this paper we reformulate and prove the stability theorems of S.M. Jung and P.K. Sahoo [S.M. Jung, P.K. Sahoo, Stability of a functional equation of Drygas, Aequationes Math. 64 (2002) 263-273] in the spaces of generalized functions such as the Schwartz distributions and tempered distributions. 相似文献
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Daryl Geller 《Journal of Functional Analysis》1980,36(2):205-254
We derive a usable characterization of the group FT (Fourier Transform) of Schwartz space on the Heisenberg group n, in terms of certain asymptotic series. To accomplish this we study in detail the FT of multiplication and differentiation operators on n, the relation of multiple Fourier series to the FT, and the process of group contraction on n. We use our characterization to solve a form of the division problem for convolution of n, which has application to Hardy space theory. 相似文献
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LetG be a locally compact group with polynomial growth and symmetricL
1-algebra andN a closed normal subgroup ofG. LetF be a closedG-invariant subset of Prim*
L
1(N) andE={ker; with |N(k(F))=0}. We prove thatE is a spectral subset of Prim*
L
1(G) ifF is spectral. Moreover we give the following application to the ideal theory ofL
1(G). Suppose that, in addition,N is CCR andG/N is compact. Then all primary ideals inL
1(G) are maximal, provided allG-orbits in Prim*
L
1(N) are spectral.Dedicated to Professor Elmar Thoma on the occasion of his 60th birthday 相似文献
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For a closed normal subgroupN of a locally compact groupG view a closed subset
of Prim*
L
1
(G/N) as a subsetE of Prim*
L
1
(G) in the canonical way and writeN
for Prim*
L
1
(G/N) as a subset of Prim*
L
1
(G); then the injection theorem says: IfE is spectral (i.e. of synthesis), then
is so; and if
andN
are spectral, thenE is too. In case of a group of polynomial growth with symmetricL
1-algebra, where smallest idealsj (E) with given hulls exist, it is known thatN
is always spectral. For a closed,G-invariant subsetF of Prim*
L
1
(N) define a closed subsetE of Prim*
L
1
(G) by
. Denote by e (I') the ideal generated byC
00
(G)*I', where theG-invariant idealI' ofL
1
(N) is viewed as a subset of measures onG, then the projection theorem states: IfE is spectral, thenF is so, and ifF is spectral withe (j (F))=j (E) thenE is spectral. All assumptions are fulfilled for instance, ifG andN are of polynomial growth with symmetricL
1-algebra and eitherSIN-groups or solvable. 相似文献
18.
We consider a nonlinear integral eigenvalue problem, which is a reformulation of the transmission eigenvalue problem arising in the inverse scattering theory. The boundary element method is employed for discretization, which leads to a generalized matrix eigenvalue problem. We propose a novel method based on the spectral projection. The method probes a given region on the complex plane using contour integrals and decides whether the region contains eigenvalue(s) or not. It is particularly suitable to test whether zero is an eigenvalue of the generalized eigenvalue problem, which in turn implies that the associated wavenumber is a transmission eigenvalue. Effectiveness and efficiency of the new method are demonstrated by numerical examples. 相似文献
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