Related papers: Multiframelet Properties on $\mathbb{Q}_p$
It is shown that any continuous function depending on several $p$-adic variables, each of which is defined on $\mathbb{Z}_{p}$, can be represented as a superposition of continuous functions of one $p$-adic variable. This statement is true…
Finite frames can be viewed as mass points distributed in $N$-dimensional Euclidean space. As such they form a subclass of a larger and rich class of probability measures that we call probabilistic frames. We derive the basic properties of…
Given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame, the frame operator is bounded, but has an unbounded…
We construct Parseval wavelet frames in $L^2(M)$ for a general Riemannian manifold $M$ and we show the existence of wavelet unconditional frames in $L^p(M)$ for $1 < p <\infty$. This is made possible thanks to smooth orthogonal projection…
This paper is devoted to wavelet analysis on adele ring $\bA$ and the theory of pseudo-differential operators. We develop the technique which gives the possibility to generalize finite-dimensional results of wavelet analysis to the case of…
We construct multiple Dirichlet series in several complex variables whose coefficients involve quadratic residue symbols. The series are shown to have an analytic continuation and satisfy a certain group of functional equations. These are…
The $p$-adic $q$-integral (= $I_q$-integral) was defined by author in the previous paper [1, 3]. In this paper, we consider $I_q$-Fourier transform and investigate some properties which are related to this transform.
In this paper we develop with considerable details a theory of multivector functions of a $p$-vector variable. The concepts of limit, continuity and differentiability are rigorously studied. Several important types of derivatives for these…
The characteristic functions of multivariate Feller processes with generator of affine type, and with smooth symbol functions have an explicit representation in terms of power series with rational number coefficients and with monmoms…
Two scaling functions $\varphi_A$ and $\varphi_B$ for Parseval frame wavelets are algebraically isomorphic, $\varphi_A \simeq \varphi_B$, if they have matching solutions to their (reduced) isomorphic systems of equations. Let $A$ and $B$ be…
We consider the notion of multiple gap as a finite set of ideals that cannot be separated. We study the different types of such objects that can be found in the Boolean algebra of subsets of the natural numbers modulo finite sets.
Let PG be the Proth-Gilbreath operator that transforms a sequence of integers into the sequence of the absolute values of the differences between all pairs of neighbor terms. Consider the infinite tables obtained by successive iterations of…
In this paper we give an attempt to extend some arithmetic properties such as multiplicativity, convolution products to the setting of operators theory. We provide a significant examples which are of interest in number theory. We also give…
Given a complex, elliptic coefficient function we investigate for which values of $p$ the corresponding second-order divergence form operator, complemented with Dirichlet, Neumann or mixed boundary conditions, generates a strongly…
We give a new class of multidimensional $p$-adic continued fraction algorithms. We propose an algorithm in the class for which we can expect that multidimensional $p$-adic version of Lagrange's Theorem holds.
We show that networks of quantum frames of reference, in which one frame may be used to produce multiple other frames that in their turn prepare systems which may interact with one another, have counterintuitive properties that make…
In this paper, we introduce a new concept of K-biframes for Hilbert spaces. We then examine several characterizations with the assistance of a biframe operator. Moreover, we investigate their properties from the perspective of operator…
Global and local regularities of functions are analyzed in anisotropic function spaces, under a common framework, that of hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities…
In this work, we investigate the role of multivalued fields in the formulation of monopole operators and their connection with topological states of matter. In quantum field theory it is known that certain states describe collective modes…
Recently, shearlet systems were introduced as a means to derive efficient encoding methodologies for anisotropic features in 2-dimensional data with a unified treatment of the continuum and digital setting. However, only very few…