Riesz potentials also called Riesz fractional derivatives and their Hilbert transforms are computed for the Korteweg-de Vries soliton. They are expressed in terms of the full-range Hurwitz Zeta functions ζ s, a and ζ− s, a . It is proved that these Riesz potentials and their Hilbert transforms are linearly independent solutions of a Sturm-Liouville problem. Various new properties are establishe...

in this paper, we first discuss about canonical dual of g-frameλp = {λip ∈ b(h, hi) : i ∈ i}, where λ = {λi ∈ b(h, hi) :i ∈ i} is a g-frame for a hilbert space h and p is the orthogonalprojection from h onto a closed subspace m. next, we provethat, if λ = {λi ∈ b(h, hi) : i ∈ i} and θ = {θi ∈ b(k, hi) :i ∈ i} be respective g-frames for non zero hilbert spaces hand k, and λ and θ are unitarily e...

Abstract In this paper we study the almost everywhere convergence of the expansions related to the self-adjoint extension of the Laplace operator. The sufficient conditions for summability is obtained. For the orders of Riesz means, which greater than critical index N−1 2 we established the estimation for maximal operator of the Riesz means. Note that when order α of Riesz means is less than cr...

This paper is an investigation of $L$-dual frames with respect to a function-valued inner product, the so called $L$-bracket product on $L^{2}(G)$, where G is a locally compact abelian group with a uniform lattice $L$. We show that several well known theorems for dual frames and dual Riesz bases in a Hilbert space remain valid for $L$-dual frames and $L$-dual Riesz bases in $L^{2}(G)$.

The present study aims at indicating the existence and uniqueness result of system in extended colombeau algebra. The Caputo fractional derivative is used for solving the system of ODEs. In addition, Riesz fractional derivative of  Colombeau generalized algebra is considered. The purpose of introducing Riesz fractional derivative is regularizing it in Colombeau sense. We also give a solution to...

In recent investigation 8] concerning the asymptotic behavior of Gram Schmidt or-thonormalization procedure applied to the nonnegative integer shifts of a given function, the problem of determining whether or not such functions form a Riesz system in L 2 (IR +) arose. In this note, we provide a suucient condition to determine whether the nonnegative translates form a Riesz system on L 2 (IR +)....

Following the approach of Chui and Quak, we investigate semi-orthogonal spline wavelets on the unit interval [0, 1]. We give a slightly different construction of boundary wavelets. As a result, we are able to prove that the inner wavelets and the newly constructed boundary wavelets together constitute a Riesz basis for the wavelet space at each level with the Riesz bounds being level-independen...

In this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet Riesz basis. The first result is an enhancement of the Paley-Wiener type constant for nonharmonic series given by Duffin and Schaefer in [6] and used recently in some applications (see [3]). In the case of an orthonormal basis our estimate reduces to Kadec’ optimal 1/4 re...

The phase computation is used in many applications of signal and image processing such as edge, line, symmetry detection, image analysis and recently to show small motion or color changes. Eulerian video processing allows to show small color changes and motions invisibles to the naked eye. Eulerian motion magnification, was modify using the phase and the Riesz pyramid in order to reduce the noi...

in this paper we proved that every g-riesz basis for hilbert space $h$ with respect to $k$ by adding a condition is a riesz basis for hilbert $b(k)$-module $b(h,k)$. this is an extension of [a. askarizadeh,m. a. dehghan, {em g-frames as special frames}, turk. j. math., 35, (2011) 1-11]. also, we derived similar results for g-orthonormal and orthogonal bases. some relationships between dual fram...