共查询到20条相似文献,搜索用时 359 毫秒
1.
H. Führ 《Advances in Computational Mathematics》2008,29(4):357-373
We derive frame bound estimates for vector-valued Gabor systems with window functions belonging to Schwartz space. The main
result provides estimates for windows composed of Hermite functions. The proof is based on a recently established sampling
theorem for the simply connected Heisenberg group, which is translated to a family of frame bound estimates via a direct integral
decomposition.
相似文献
2.
Francesca Astengo 《Journal of Functional Analysis》2009,256(5):1565-2814
Let Hn be the (2n+1)-dimensional Heisenberg group and K a compact group of automorphisms of Hn such that (K?Hn,K) is a Gelfand pair. We prove that the Gelfand transform is a topological isomorphism between the space of K-invariant Schwartz functions on Hn and the space of Schwartz function on a closed subset of Rs homeomorphic to the Gelfand spectrum of the Banach algebra of K-invariant integrable functions on Hn. 相似文献
3.
The aim of this paper is to obtain certain characterizations for the image of a Sobolev space on the Heisenberg group under the heat kernel transform. We give three types of characterizations for the image of a Sobolev space of positive order $H^m(\mathbb {H}^n), m\in \mathbb {N}^n,$ under the heat kernel transform on $\mathbb {H}^n,$ using direct sum and direct integral of Bergmann spaces and certain unitary representations of $\mathbb {H}^n$ which can be realized on the Hilbert space of Hilbert‐Schmidt operators on $L^2(\mathbb {R}^n).$ We also show that the image of Sobolev space of negative order $H^{-s}(\mathbb {H}^n), s(>0) \in \mathbb {R}$ is a direct sum of two weighted Bergman spaces. Finally, we try to obtain some pointwise estimates for the functions in the image of Schwartz class on $\mathbb {H}^n$ under the heat kernel transform. 相似文献
4.
In this paper we continue our work on Schwartz functions and generalized Schwartz functions on Nash (i.e. smooth semi-algebraic)
manifolds. Our first goal is to prove analogs of the de-Rham theorem for de-Rham complexes with coefficients in Schwartz functions
and generalized Schwartz functions. Using that we compute the cohomologies of the Lie algebra g of an algebraic group G with coefficients in the space of generalized Schwartz sections of G-equivariant bundle over a G-transitive variety M. We do it under some assumptions on topological properties of G and M. This computation for the classical case is known as the Shapiro lemma. 相似文献
5.
In this note we present a symbolic pseudo-differential calculus on the Heisenberg group. We particularise to this group our general construction [4], [2] and [3] of pseudo-differential calculi on graded groups. The relation between the Weyl quantisation and the representations of the Heisenberg group enables us to consider here scalar-valued symbols. We find that the conditions defining the symbol classes are similar but different to the ones in [1]. Applications are given to Schwartz hypoellipticity and to subelliptic estimates on the Heisenberg group. 相似文献
6.
We obtain the Plancherel decomposition for a reductive symmetric space in the sense of representation theory. Our starting point is the Plancherel formula for spherical Schwartz functions, obtained in part I. The formula for Schwartz functions involves Eisenstein integrals obtained by a residual calculus. In the present paper we identify these integrals as matrix coefficients of the generalized principal series. 相似文献
7.
We give an overview on surjectivity conditions for partial differential operators and operators defined by multiplication with polynomials on certain function and distribution spaces of Laurent Schwartz. We complement the classical results by treating the surjectivity of operators on the space of slowly increasing functions and on the space of rapidly decreasing distributions, respectively. 相似文献
8.
A. V. Stoyanovskii 《Functional Analysis and Its Applications》2006,40(3):241-243
We describe the image of the Weil representation of the double covering of the symplectic group in the Schwartz space in the so-called geometric realization, i.e., in holomorphic functions on the symmetric domain called the Siegel upper half-plane. 相似文献
9.
Nils Byrial Andersen 《Journal of Fourier Analysis and Applications》2006,12(1):17-25
We first characterize the image of the compactly supported smooth even functions under the Hankel transform as a subspace
of the Schwartz space. We then describe the space of smooth Lp-functions whose Hankel transform has compact support as a subspace of the space of
Lp-functions. 相似文献
10.
We construct an algebra of generalized functions endowed with a canonical embedding of the space of Schwartz distributions.We offer a solution to the problem of multiplication of Schwartz distributions similar to but different from Colombeau’s solution.We show that the set of scalars of our algebra is an algebraically closed field unlike its counterpart in Colombeau theory, which is a ring with zero divisors. We prove a Hahn–Banach extension principle which does not hold in Colombeau theory. We establish a connection between our theory with non-standard analysis and thus answer, although indirectly, a question raised by Colombeau. This article provides a bridge between Colombeau theory of generalized functions and non-standard analysis. 相似文献
11.
We prove a generalization of the Littlewood–Paley characterisation of the BMO space where the shifts of a Schwartz function are replaced by a family of functions with suitable conditions imposed on them. We also prove that a certain family of Triebel–Lizorkin spaces can be characterized in a similar way. 相似文献
12.
13.
Kehe Zhu 《Bulletin des Sciences Mathématiques》2011,(5):467
We show that there is only one non-trivial Hilbert space of entire functions that is invariant under the action of a certain unitary representation of the Heisenberg group. 相似文献
14.
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.
15.
In this paper we study the Hankel convolution operators on the space of even and entire functions and on Schwartz distribution spaces. We characterize the Hankel convolution operators as those ones that commute with Hankel translations and with a Bessel operator. Also we prove that the Hankel convolution operators are hypercyclic and chaotic on the spaces under consideration. 相似文献
16.
Roberto Monti 《Journal of Geometric Analysis》2014,24(4):1673-1715
We prove several rearrangement theorems in the setting of a metric measure space. We adapt the general scheme of the argument to the Heisenberg group, where we study Steiner and circular rearrangement for functions and sets having a suitable symmetry. 相似文献
17.
We describe several different representations of nilpotent step two Lie groups in spaces of monogenic Clifford‐valued functions. We are inspired by the classic representation of the Heisenberg group in the Segal–Bargmann space of holomorphic functions. Connections with quantum mechanics are described. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
18.
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
19.
We discuss the octonionic regular functions and the octonionic regular operator on the octonionic Heisenberg group. This is the octonionic version of CR function theory in the theory of several complex variables and regular function theory on the quaternionic Heisenberg group. By identifying the octonionic algebra with \(\mathbb{R }^{8}\) , we can write the octonionic regular operator and the associated Laplacian operator as real \((8\times 8)\) -matrix differential operators. Then we use the group Fourier transform on the octonionic Heisenberg group to analyze the associated Laplacian operator and to construct its kernel. This kernel is exactly the Szegö kernel of the orthonormal projection from the space of \(L^{2}\) functions to the space of \(L^{2}\) regular functions on the octonionic Heisenberg group. 相似文献
20.
In this article we provide several generalizations of inequalities bounding the commutator of two linear operators acting on a Hilbert space which relate to the Heisenberg uncertainty principle and time/frequency analysis of periodic functions. We develop conditions that ensure these inequalities are sharp and apply our results to concrete examples of importance in the literature. 相似文献