Related papers: Discrete fractional integral operators with binary…
The fractional integrals and fractional derivatives problem is tackled by using the operator approach. The definition domain E of operators is causal functions.Many properties of fractional integrals are given. Fractional derivatives…
We present a construction of a large class of Laplace invariants for linear hyperbolic partial differential operators of fairly general form and arbitrary order.
We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and $q$-difference equations for these polynomials. A general functional equation is found which allows one to relate…
A general scheme for tridiagonalising differential, difference or q-difference operators using orthogonal polynomials is described. From the tridiagonal form the spectral decomposition can be described in terms of the orthogonality measure…
We obtain $L^2$ decay estimates in $\lambda$ for oscillatory integral operators whose phase functions are homogeneous polynomials of degree m and satisfy various genericity assumptions. The decay rates obtained are optimal in the case of…
This paper is devoted to the study of quasi-periodic properties of fractional order integrals and derivatives of periodic functions. Considering Riemann-Liouville and Caputo definitions, we discuss when the fractional derivative and when…
After reviewing the definition of two differential operators which have been recently introduced by Caputo and Fabrizio and, separately, by Atangana and Baleanu, we present an argument for which these two integro-differential operators can…
Through examples, we illustrate how to compute differential operators on a quotient of an affine semigroup ring by a radical monomial ideal, when working over an algebraically closed field of characteristic 0.
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
The aim of this article is to present a complete system of Floquet spectral invariants for the discrete Schr\"odinger operators with periodic potentials on periodic graphs. These invariants are polynomials in the potential and determined by…
We consider a class of pseudodifferential operators with a doubly characteristic point, where the quadratic part of the symbol fails to be elliptic but obeys an averaging assumption. Under suitable additional assumptions, semiclassical…
We consider fractional differentiation operators in various senses and show that the strictly accretive property is the common property of fractional differentiation operators. Also we prove that the sectorial property holds for…
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…
We consider kernels of discrete convolution operators or, equivalently, homogeneous solutions of partial difference operators and show that these solutions always have to be exponential polynomials. The respective polynomial space in…
We study the Hp-Lq boundedness of certain integral operators of fractional type.
In this paper we explore the theory of fractional powers of non-negative (and not necessarily self-adjoint) operators and its amazing relationship with the Chebyshev polynomials of the second kind to obtain results of existence, regularity…
We elucidate why an interval algorithm that computes the exact bounds on the amplitude and phase of the discrete Fourier transform can run in polynomial time. We address this question from a formal perspective to provide the mathematical…
We prove global subelliptic estimates for quadratic differential operators. Quadratic differential operators are operators defined in the Weyl quantization by complex-valued quadratic symbols. In a previous joint work with M. Hitrik, we…
In these expository notes we draw together and develop the ideas behind some recent progress in two directions: the treatment of finite type partial differential operators by prolongation, and a class of differential complexes known as…
Explicit evaluations of matrix-variate gamma and beta integrals in the complex domain by using conventional procedures is extremely difficult. Such an evaluation will reveal the structure of these matrix-variate integrals. In this article,…