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We study large deviation properties of random matricial spectral measures.
Motivated by the multivariate wavelet theory, and by the spectral theory of transfer operators, we construct an abstract affine structure and a multiresolution associated to a matrix-valued weight. We describe the one-to-one correspondence…
In this paper orthogonal multifilters for astronomical image processing are presented. We obtained new orthogonal multifilters based on the orthogonal wavelet of Haar and Daubechies. Recently, multiwavelets have been introduced as a more…
This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous…
Multidimensional contractions of irreducible representations of Cayley--Klein orthogonal algebras in Gel'fand--Zetlin basis are considered. Contracted over different parameters, algebras can turn out to be isomorphic. In this case method of…
We show that any $L^2$-bounded rational function in free semicircular random variables is a bounded operator, which implies the coincidence of the usual spectrum and $L^2$-spectrum for rational functions. Based on this observation, we also…
Two properties of Calogero wave functions for rational Calogero models are studied: (i) the representation of the wave functions in terms of the exponential of Lassalle operators, (ii) the $sL(2,\rr)$ structure of the Calogero--Moser wave…
We present the application of the variational-wavelet analysis to the quasiclassical calculations of the solutions of Wigner/von Neumann/Moyal and related equations corresponding to the nonlinear (polynomial) dynamical problems. (Naive)…
We study orthogonal polynomials for a weight function defined over a domain of revolution, where the domain is formed from rotating a two-dimensional region and goes beyond the quadratic domains. Explicit constructions of orthogonal bases…
In the paper the general case of a normal discrete Hausdorff operators in $L^2(\mathbb{R}^d)$ is considered. The main result states that under some natural arithmetic condition the spectrum of such an operator is rotationally invariant.…
Hyperspectral Imaging is a crucial tool in remote sensing which captures far more spectral information than standard color images. However, the increase in spectral information comes at the cost of spatial resolution. Super-resolution is a…
Alternative expressions for calculating the oblate spheroidal radial functions of both kinds R1ml and R2ml are shown to provide accurate values over very large parameter ranges using 64 bit arithmetic, even where the traditional expressions…
In this paper, some ?-classes of weighted conditional expectation type operators, such as A-class, ?-A-class and quasi-?-A classes on L2(?) are investigated. Also, the spectrum, point spectrum and spectral radius of these operators are…
The differential-geometric and topological structure of Delsarte transmutation operators and associated with them Gelfand-Levitan-Marchenko type eqautions are studied making use of the De Rham-Hodge-Skrypnik differential complex. The…
We construct an explicit orthonormal basis of piecewise ${}_{i+1}F_{i}$ hypergeometric polynomials for the Alpert multiresolution analysis. The Fourier transform of each basis function is written in terms of ${}_2F_3$ hypergeometric…
Structure constants of Operator Algebras for the SL(2) degenerate conformal field theories are calculated.
Reduction operators, i.e. the operators of nonclassical (or conditional) symmetry of a class of variable coefficient nonlinear wave equations with power nonlinearities is investigated within the framework of singular reduction operator. A…
The Haar functional on the quantum $SU(2)$ group is the analogue of invariant integration on the group $SU(2)$. If restricted to a subalgebra generated by a self-adjoint element the Haar functional can be expressed as an integral with a…
This note is devoted to optimal spectral estimates for Schr\"odinger operators on compact connected Riemannian manifolds without boundary. These estimates are based on the use of appropriate interpolation inequalities and on some recent…
A complete characterisation is given of all the linear isometries of the Fr\'echet space of all holomorphic functions on the unit disc, when it is given one of the two standard metrics: these turn out to be weighted composition operators of…