Related papers: Unconditionally convergent multipliers and Bessel …
Multipliers are operators that combine (frame-like) analysis, a multiplication with a fixed sequence, called the symbol, and synthesis. They are very interesting mathematical objects that also have a lot of applications for example in…
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…
In this paper we ask when it is possible to transform a given sequence into a frame or a lower semi frame by multiplying the elements by numbers. In other words, we ask when a given sequence is a weighted frame or a weighted lower semi…
We prove that if every element $u$ in a Hilbert space $H$ admits a representation as unconditionally convergent series $$u=\sum_{k=1}^\infty \langle u, y_k\rangle x_k,$$ then there exist nonzero scalars $\{\alpha_k\}_{k=1}^\infty$ such that…
We prove the Feichtinger Conjecture for a class of Bessel sequences of unit norm vectors in a Hilbert space. Also, we prove that every Bessel sequence of unit vectors in a Hilbert space can be partitioned into finitely many uniformly…
It is shown that the algebraic structure of finite Heisenberg groups associated with the tensor product of two Hilbert spaces leads to a simple demonstration valid in all Hilbert space dimensions of the impossibility of non-contextual…
In this paper we investigate the possibility of unconditional convergence and invertibility of multipliers $M_{m,\Phi,\Psi}$ depending on the properties of the sequences $\Psi$,$\Phi$ and $m$. We characterize a complete set of conditions…
We introduce the notion of a continuous biframe in a Hilbert space which is a generalization of discrete biframe in Hilbert space. Representation theorem for this type of generalized frame is verified and some characterizations of this…
It is known that the tensor product of two sequences, in the tensor product of two separable Hilbert spaces, is a frame if and only if each component of that product is a frame. This paper proposes a sort of generalization of the…
In this paper we study the concept of multipliers for continuous $g$-Bessel families in Hilbert spaces. We present necessary conditions for invertibility of multipliers for continuous $g$-Bessel families and sufficient conditions for…
We prove that any complete metric space has a unique decomposition as a direct product of a possibly finite or zero-dimensional Hilbert space and a space that does not split off lines.
Let $G$ be an infinite locally compact abelian group. If $X$ is Banach space, we show that if every bounded Fourier multiplier $T$ on $L^2(G)$ has the property that $T\ot Id_X$ is bounded on $L^2(G,X)$ then the Banach space $X$ is…
Let $U(\mathbb T)$ be the space of all continuous functions on the circle $\mathbb T$ whose Fourier series converges uniformly. Salem's well-known example shows that a product of two functions in $U(\mathbb T)$ does not always belongs to…
The notation of generalized Bessel multipliers is obtained by a bounded operator on $\ell^2$ which is inserted between the analysis and synthesis operators. We show that various properties of generalized multipliers are closely related to…
The paper presents a survey over frame multipliers and related concepts. In particular, it includes a short motivation of why multipliers are of interest to consider, a review as well as extension of recent results, devoted to the…
The most fundamental notion in frame theory is the frame expansion of a vector. Although it is well known that these expansions are unconditionally convergent series, no characterizations of the unconditional constant were known. This has…
We prove two new equivalences of the Feichtinger conjecture that involve reproducing kernel Hilbert spaces. We prove that if for every Hilbert space, contractively contained in the Hardy space, each Bessel sequence of normalized kernel…
The paper discusses a series of results concerning reproducing kernel Hilbert spaces, related to the factorization of their kernels. In particular, it is proved that for a large class of spaces isometric multipliers are trivial. One also…
In this paper we show that every g-frame for an \linebreak infinite dimensional Hilbert space $\mathcal{H}$ can be written as a sum of three g-orthonormal bases for $\mathcal{H}$. Also, we prove that every g-frame can be represented as a…
We introduce the notion of continuous frame in n-Hilbert space which is a generalization of discrete frame in n-Hilbert space. The tensor product of Hilbert spaces is a very important topic in mathematics. Here we also introduce the concept…