相关论文: How to construct wavelets on local fields of posit…
The concept of super-wavelet was introduced by Balan, and Han and Larson over the field of real numbers which has many applications not only in engineering branches but also in different areas of mathematics. To develop this notion on local…
The main objective of this paper is to define the mother wavelet on local fields and study the continuous wavelet transform (CWT) and some of their basic properties. its inversion formula, the Parseval relation and associated convolution…
In the present paper, a construction of spin weighted spherical wavelets is presented. It is based on approximate identities, the wavelets are defined for a continuous set of parameters, and the wavelet transform is invertible directly by…
Using a prime element of a local field K of positive characteristic p, the concepts of multiresolution analysis (MRA) and wavelet can be generalized to such a field. We prove a version of the splitting lemma for this setup and using this…
Due to their adaptive nature, empirical wavelets had several successes in many fields from engineering, science, medical signal/image processing. Recently, a general theoretical framework has been developed in the one-dimensional case,…
This note provides new methods for constructing quadratic nonresidues in finite fields of characteristic p. It will be shown that there is an effective deterministic polynomial time algorithm for constructing quadratic nonresidues in finite…
A constructive algorithm based on the theory of spectral pairs for constructing nonuniform wavelet basis in $L^2(\mathbb R)$ was considered by Gabardo and Nashed (J Funct. Anal. 158:209-241, 1998). In this setting, the associated…
We present a construction of biorthogonal wavelets using a compact operator which allows to preserve or increase some properties: regularity/vanishing moments, parity, compact supported. We build then a simple algorithm which computes new…
We revisit the feasibility approach to the construction of compactly supported smooth orthogonal wavelets on the line. We highlight its flexibility and illustrate how symmetry and cardinality properties are easily embedded in the design…
In integrable models of quantum field theory, local fields are normally constructed by means of the bootstrap-formfactor program. However, the convergence of their $n$-point functions is unclear in this setting. An alternative approach uses…
We develop a weighted local likelihood estimate for the parameters that govern the local spatial dependency of a locally stationary random field. The advantage of this local likelihood estimate is that it smoothly downweights the influence…
We present a new scheme for the construction of highly localized lattice Wannier functions. The approach is based on a heuristic criterion for localization and takes the symmetry constraints into account from the start. We compare the local…
In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be "dilated" by a procedure comparable to the operation…
The development of interatomic potentials that can accurately capture a wide range of physical phenomena and diverse environments is of significant interest, but it presents a formidable challenge. This challenge arises from the numerous…
This paper deals with the problem of classifying signals. The new method for building so called local classifiers and local features is presented. The method is a combination of the lifting scheme and the support vector machines. Its main…
Let G be a locally compact abelian group with compact open subgroup H. The best known example of such a group is G=Q_p, the field of p-adic rational numbers (as a group under addition), which has compact open subgroup H=Z_p, the ring of…
In this article, we develop a general method for constructing wavelets {|det A_j|^{1/2} g(A_jx-x_{j,k}): j in J, k in K}, on irregular lattices of the form X={x_{j,k} in R^d: j in J, k in K}, and with an arbitrary countable family of…
It is given an efficient complete parametrization of wavelet matrices of rank $m$, genus $g+1$, and degree $g$, which are naturally identified with corresponding polynomial paraunitary matrix-functions. The parametrization depends on…
We introduce an orbifold induction procedure which provides a systematic construction of cyclic orbifolds, including their twisted sectors. The procedure gives counterparts in the orbifold theory of all the current-algebraic constructions…
The main contribution of this paper is a constructive method for building separable multivariate vector-valued wavelet bases in the general framework of \( L^2(\mathbb{R}^d, \mathbb{R}^m) \) for any \( d, m \geq 1 \). While separable…