相关论文: Generalized Fourier representation of the absolute…
We introduce a simple, general, and convergent scheme to compute generalized eigenfunctions of self-adjoint operators with continuous spectra on rigged Hilbert spaces. Our approach does not require prior knowledge about the eigenfunctions,…
We consider an arbitrary selfadjoint operator on a separable Hilbert space. To this operator we construct an expansion in generalized eigenfunctions in which the original Hilbert space is decomposed as a direct integral of Hilbert spaces…
New sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained in the paper.
We prove explicitly that to every discrete, semibounded Hamiltonian with constant degeneracy and with finite sum of the squares of the reciprocal of its eigenvalues and whose eigenvectors span the entire Hilbert space there exists a…
It is well established that the physical phenomenon of intermittency can be investigated via the spectral analysis of a transfer operator associated with the dynamics of an interval map with indifferent fixed point. We present here for the…
In this paper we obtain new sufficient conditions for representation of a function as an absolutely convergent Fourier integral. Unlike those known earlier, these conditions are given in terms of belonging to weighted spaces. Adding weights…
This paper examines the existence and region of convergence of Fourier transform of the functions of bicomplex variables with the help of projection on its idempotent components as auxiliary complex planes. Several basic properties of this…
Fourier representation (FR) is an indispensable mathematical formulation for modeling and analysis of physical phenomenon, engineering systems and signals in numerous applications. In this study, we present the generalized Fourier…
We give a generalization of the Jordan canonical form theorem for a class of bounded linear operators on complex separable Hilbert spaces in terms of direct integrals. Precisely, we study the uniqueness of strongly irreducible…
This article addresses linear hyperbolic partial differential equations and pseudodifferential equations with strongly singular coefficients and data, modelled as members of algebras of generalised functions. We employ the recently…
We study an extension to Fourier transforms of the old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series. The results are obtained by revealing…
We study finitely cyclic self-adjoint operators in a Hilbert space, i.e. self-adjoint operators that posses such a finite subset in the domain that the orbits of all its elements with respect to the operator are linearly dense in the space.…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
It is shown that any real and even function of the phase (time) operator has a self-adjoint extension and its relation to the general phase operator problem is analyzed.
New sufficient conditions for representation of a function via the absolutely convergent Fourier integral are obtained in the paper. In the main result, Theorem 1.1, this is controlled by the behavior near infinity of both the function and…
We construct a calculus for generalized $\mathbf{SG}$ Fourier integral operators, extending known results to a broader class of symbols of $\mathbf{SG}$ type. In particular, we do not require that the phase functions are homogeneous. We…
In this paper spectral theorems for not necessarily continuous normal and self-adjoint random operators on a complex separable Hilbert space are proved.
We survey our recent result that for every continuous function there is an absolutely continuous homeomorphism such that the composition has a uniformly converging Fourier expansion. We mention the history of the problem, orginally stated…
In this work we define operator-valued Fourier transforms for suitable integrable elements with respect to the Plancherel weight of a (not necessarily Abelian) locally compact group. Our main result is a generalized version of the Fourier…
We consider the irreducibility of the regular representation of a noncompact semisimpe Lie group $G$ on the Hilbert space of the image of the Joint-Eigenspace Fourier transform on its corresponding symmetric space $G/K.$ The…