Related papers: p-Adic refinable functions and MRA-based wavelets
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…
After recalling the notion of Lie algebroid, we construct these structures associated with contact forms or systems. We are then interested in particular classes of Lie Rinehart algebras.
In the present paper, multiscale systems of polynomial wavelets on an n-dimensional sphere are constructed. Scaling functions and wavelets are investigated,and their reproducing and localization properties and positive definiteness are…
We develop the theory of p-Lie algebras of finite Morley rank. In particular, we obtain a quite complete characterization in the soluble case
By interpreting planar polynomial curves as complex-valued functions of a real parameter, an inner product, norm, metric function, and the notion of orthogonality may be defined for such curves. This approach is applied to the complex…
We introduce a new concept of the so-called {\it composite wavelet transforms}. These transforms are generated by two components, namely, a kernel function and a wavelet function (or a measure). The composite wavelet transforms and the…
The free Baker-Akhiezer modules on rational varieties obtained from ${\mathbb C}P^{1}\times{\mathbb C}P^{n-1}$ by identification of two hypersurfaces are constructed. The corollary of this construction is the existence of embedding of…
In this brief note, we consider p-adic unit roots or poles of L-functions of exponential sums defined over finite fields. In particular, we look at the number of unit roots or poles, and a congruence relation on the units. This raises a…
We present an efficient algorithm for computing certain special values of Rankin triple product $p$-adic L-functions and give an application of this to the explicit construction of rational points on elliptic curves.
The problem of backward dynamics over the ring of p-adic integers is studied. It is shown that Inverse Limit Theory provides the right framework. Backward iterations of a polynomial with p-adic integer coefficients are constructed by…
We introduce the notion of extended affine Lie superalgebras and investigate the properties of their root systems. Extended affine Lie algebras, invariant affine reflection algebras, finite dimensional basic classical simple Lie…
We describe a method to construct directed networks from multivariate time series which has several advantages over the widely accepted methods. This method is based on an information theoretic reduction of linear (auto-regressive) models.…
In this paper novel classes of 2-D vector-valued spatial domain wavelets are defined, and their properties given. The wavelets are 2-D generalizations of 1-D analytic wavelets, developed from the Generalized Cauchy-Riemann equations and…
In this paper, we describe some recent results obtained in the context of vector subdivision schemes which possess the so-called full rank property. Such kind of schemes, in particular those which have an interpolatory nature, are connected…
Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP…
In this paper we will investigate properties of modified q-Euler numbers and polynomials. The main purpose of this paper is to construct p-adic q-Euler measures.
We compute, in a stable range, the arithmetic p-adic etale cohomology of smooth rigid analytic and dagger varieties (without any assumption on the existence of a nice integral model) in terms of differential forms using syntomic methods.…
In this paper we present a general approach to multivariate periodic wavelets generated by scaling functions of de la Vall\'ee Poussin type. These scaling functions and their corresponding wavelets are determined by their Fourier…
The main objective of this article is to establish the $p$-adic Artin formalism for the algebraic $p$-adic $L$-functions attached to the adjoint representations of Coleman families of modular forms. In particular, we prove a factorization…
In this paper we present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to variational approach in the general case we have the solution as a…