相关论文: Bochner PG-Frames

Using methods of descriptive set theory, in particular, the determinacy of infinite games of perfect information, we answer several questions from the literature regarding different notions of bases in Banach spaces and lattices. For the…

A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certain Banach spaces. Many classical function…

In this paper we introduce the notion of property $(BR)$ and property $(BgR)$ for bounded linear operators defined on an infinite-dimensional Banach space. These properties in connection with Weyl type theorems and in the frame of polaroid…

This paper studies Hausdorff-Young-type inequalities within the framework of Lorentz spaces $L_{p,q}$. Focusing on the dependence of the associated constants on the integrability parameter $p$, we derive optimal bounds in the limiting case…

In this paper, we propose to define the concept of family of local atoms and then we generalize this concept to the atomic system for operator in Banach spaces by using semi-inner product. We also give a characterization of atomic systems…

We develope a local theory for frames on finite dimensional Hilbert spaces. In particular, a bounded frame on a finite dimensional Hilbert space contains a subset which is a good Riesz basis for a percentage (arbitrarily close to one) of…

The main purpose of this paper is to investigate the concept of maximal $L^p$-regularity for perturbed evolution equations in Banach spaces. We mainly consider three classes of perturbations: Miyadera-Voigt perturbations, Desch-Schappacher…

In analogy with bilinear Riesz potentials, we introduce bilinear Bessel potentials and characterize their boundedness from $L^p\times L^q$ into Lebesgue and Lorentz spaces $L^{r,\alpha}.$ In several cases we identify the optimal Lorentz…

We develop a usable perturbation theory for Weyl-Heisenberg frames. In particular, we prove that if $(E_{mb}T_{na}g)_{m,n\inmathbb Z}$ is a WH-frame and $h$ is a function which is close to $g$ in the Wiener Amalgam space norm, then…

In this paper, we introduce the concept of semi-continuous $g$-frames in Hilbert spaces. We first construct an example of semi-continuous $g$-frames using the Fourier transform of the Heisenberg group and study the structure of such frames.…

We study the complexity of Banach space valued integration in the randomized setting. We are concerned with $r$-times continuously differentiable functions on the $d$-dimensional unit cube $Q$, with values in a Banach space $X$, and…

This paper is concerned with the characterization of $\alpha$-modulation spaces by Banach frames, i.e., stable and redundant non-orthogonal expansions, constituted of functions obtained by a suitable combination of translation, modulation…

We define an {\it $(X_1,\Theta, X_2)$-frame} with Banach spaces $X_2\subseteq X_1$, $|\cdot|_1 \leq |\cdot|_2$, and a $BK$-space $(\Theta, \snorm[\cdot])$. Then by the use of decreasing sequences of Banach spaces ${X_s}_{s=0}^\infty$ and of…

We prove that a Hilbert space frame $\fti$ contains a Riesz basis if every subfamily $\ftj , J \subseteq I ,$ is a frame for its closed span. Secondly we give a new characterization of Banach spaces which do not have any subspace isomorphic…

We study lower bounds for the norm of the product of polynomials and their applications to the so called \emph{plank problem.} We are particularly interested in polynomials on finite dimensional Banach spaces, in which case our results…

One approach to ease the construction of frames is to first construct local components and then build a global frame from these. In this paper we will show that the study of the relation between a frame and its local components leads to the…

We characterize Riesz frames and frames with the subframe property and use this to answer most of the questions from the literature concerning these properties and their relationships to the projection methods etc.

P representation techniques, which have been very successful in quantum optics and in other fields, are also useful for general bosonic quantum dynamical many-body calculations such as Bose-Einstein condensation. We introduce a…

Motivated by the problem of spherical summability of products of Fourier series, we study the boundedness of the bilinear Bochner-Riesz multipliers $(1-|\xi|^2-|\eta|^2)^\delta_+$ and we make some advances in this investigation. We obtain…

This paper generalizes results for alternate dual frames in Hilbert spaces on the situation of a Banach space. Additionally some properties of synthesys operator associated with alternate dual frame are investigated. The main result is that…