Related papers: Frames and representing systems in Fr\'echet space…
This paper introduces the concept of Bessel multipliers. These operators are defined by a fixed multiplication pattern, which is inserted between the Analysis and synthesis operators. The proposed concept unifies the approach used for Gabor…
Braided sets which are also spaces with dilations are presented and explored in this paper, in the general frame of emergent algebras arxiv:0907.1520. Examples of such spaces are the sub-riemannian symmetric spaces. Keywords: braided sets,…
We introduce and develop the concept of oblique duality for fusion frames. This concept provides a mathematical framework to deal with problems in distributed signal processing where the signals, considered as elements in a Hilbert space…
Fr\'echet mean and variance provide a way of obtaining mean and variance for general metric space valued random variables and can be used for statistical analysis of data objects that lie in abstract spaces devoid of algebraic structure and…
We consider a trace theorem for self-similar Dirichlet forms on self-similar sets to self-similar subsets. In particular, we characterize the trace of the domains of Dirichlet forms on the Sierpinski gaskets and the Sierpinski carpets to…
We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable…
Shearlet systems have so far been only considered as a means to analyze $L^2$-functions defined on $\R^2$, which exhibit curvilinear singularities. However, in applications such as image processing or numerical solvers of partial…
Given a sequence of finite element spaces which form a de Rham sequence, we will construct a dual representation of these spaces with associated differential operators which connect these spaces such that they also form a de Rham sequence.…
We discuss analogies between number theory and the theory of dynamical systems on spaces with a one-codimensional foliation. The emphasis is on comparing the "explicit formulas" of analytic number theory with certain dynamical Lefschetz…
This paper deals with fractional-order controlled systems and fractional-order controllers in the frequency domain. The mathematical description by fractional transfer functions and properties of these systems are presented. The new ways…
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…
The aim of this paper is to present a new simple recurrence for Appell and Sheffer sequences in terms of the linear functional that defines them, and to explain how this is equivalent to several well-known characterizations appearing in the…
Fractional spline wavelet systems are considered in the work. Molecular structure of elements of such systems admits estimates connecting norms of fractional integrals' images and pre--images in Besov spaces.
We consider evolution differential equations in Fr\'echet spaces that possess unconditional Schauder basis and construct a version of the majorant functions method to obtain existence theorems for Cauchy problems. Applications to PDE and…
We analyze the construction of a sequence space $\widetilde{\Theta}$, resp. a sequence of sequence spaces, in order to have $\{g_i\}$ as a $\widetilde{\Theta}$-frame or Banach frame for a Banach space $X$, resp. pre-$F$-frame or $F$-frame…
Dynamical Sampling of frames and tensor products are important topics in harmonic analysis. This paper combines the concepts of dynamical sampling of frames and the Carleson condition in the tensor product of Hardy spaces. Initially we…
Every frame in Hilbert space contains a subsequence equivalent to an orthogonal basis. If a frame is n-dimensional then this subsequence has length (1 - \epsilon) n. On the other hand, there is a frame which does not contain bases with…
The goal of the present paper is to extend the theory of frames for countably generated Hilbert $C^*$-modules over arbitrary $C^*$-algebras. In investigating the non-unital case we introduce the concept of outer frame as a sequence in the…
Stochastic processes are considered on free loop spaces, geometric loop and diffeomorphism groups of real and complex manifolds. They are used for investigations of Wiener differentiable quasi-invariant measures on such groups relative to…
We consider translates of functions in $L^2(\RRd)$ along an irregular set of points. Introducing a notion of pseudo-Gramian function for the irregular case, we obtain conditions for a family of irregular translates to be a Bessel sequence…