Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSome notes about distribution frame multipliers
68
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Inspired by a recent work about distribution frames, the definition of multiplier operator is extended in the rigged Hilbert spaces setting and a study of its main properties is carried on. In particular, conditions for the density of domain and boundedness are given. The case of Riesz distribution bases is examined in order to develop a symbolic calculus.
rate research
Read More
A dual frames multiplier is an operator consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames in a Hilbert space, respectively. In this paper we investigate the spectra of some dual frames multipliers giving, in particular, conditions to be at most countable. The contribution extends the results available in literature about the spectra of Bessel multipliers with symbol decaying to zero and of multipliers of dual Riesz bases.
Let D be a masa in B(H) where H is a separable Hilbert space. We find real numbers eta_0 < eta_1 < eta_2 < ... < eta_6 so that for every bounded, normal D-bimodule map {Phi} on B(H) either ||Phi|| > eta_6, or ||Phi|| = eta_k for some k <= 6. When D is totally atomic, these maps are the idempotent Schur multipliers and we characterise those with norm eta_k for 0 <= k <= 6. We also show that the Schur idempotents which keep only the diagonal and superdiagonal of an n x n matrix, or of an n x (n+1) matrix, both have norm 2/(n+1) cot(pi/(n+1)), and we consider the average norm of a random idempotent Schur multiplier as a function of dimension. Many of our arguments are framed in the combinatorial language of bipartite graphs.
In this article we examine Dirichlet type spaces in the unit polydisc, and multipliers between these spaces. These results extend the corresponding work of G. D. Taylor in the unit disc. In addition, we consider functions on the polydisc whose restrictions to lower dimensional polydiscs lie in the corresponding Dirichet type spaces. We see that such functions need not be in the Dirichlet type space of the whole polydisc. Similar observations are made regarding multipliers.
In the present paper the unconditional convergence and the invertibility of multipliers is investigated. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or necessary conditions for unconditional convergence and invertibility are determined depending on the properties of the analysis and synthesis sequences, as well as the symbol. Examples which show that the given assertions cover different classes of multipliers are given. If a multiplier is invertible, a formula for the inverse operator is determined. The case when one of the sequences is a Riesz basis is completely characterized.
The main purpose of this paper is to prove Hormanders $L^p$-$L^q$ boundedness of Fourier multipliers on commutative hypergroups. We carry out this objective by establishing Paley inequality and Hausdorff-Young-Paley inequality for commutative hypergroups. We show the $L^p$-$L^q$ boundedness of the spectral multipliers for the generalised radial Laplacian by examining our results on Ch{e}bli-Trim`{e}che hypergroups. As a consequence, we obtain embedding theorems and time asymptotics for the $L^p$-$L^q$ norms of the heat kernel for generalised radial Laplacian. Finally, we present applications of the obtained results to study the well-posedness of nonlinear partial differential equations.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
