Abstract Motivated by the recent studies and developments of integral transforms with various special matrix functions, including orthogonal polynomials as kernels, in this article we derive formulas for Fourier cosine sine functions involving generalized Bessel polynomials. With help these several results are obtained, which extensions corresponding standard cases. The given here general chara...

The paper presents a survey of results related to continuity properties of dyadic integrals used in solving the problem of recovering, by generalized Fourier formulas, the coefficients of series with respect to multiple Haar and Walsh systems.

In this paper, a known theorem dealing with | N̄, pn |k summability factors of trigonometric Fourier series has been generalized to | N̄, pn, θn |k summability. Some new results have also been obtained.

The behavior of generalized Cesàro (C, αn)-means (αn ∈ (−1, 0), n = 1, 2, . . . ) of conjugate trigonometric Fourier series of H classes in the space of continuous functions is studied. 2000 Mathematics Subject Classification: 42A50.

A Fourier-collocation scheme is used to approximate solutions to the generalized Benjamin-Ono equation ut +uux −Huxx = 0. The numerical simulation suggests that the equation features smooth solutions that become unbounded in finite time.

A new theorem on almost generalized Nörlund summability of conjugate series of Fourier series has been established under a very general condition. 2000 Mathematics Subject Classification. Primary 42B05, 42B08.

We derive and discuss the analytical solution for the generalized time-fractional telegraph equation with the help of the Sumudu and Fourier transforms. In the process we use Green functions to derive the solution of the said differential equation.

FRACTIONAL FOURIER INTEGRAL THEOREM AND FRACTIONAL FOURIER SINE AND COSINE TRANSFORM Saleem Iqbal, S.M. Raza, * LalaRukh Kamal and Farhana Sarwar Department of Mathematics/Physics, University of Balochistan, Quetta, Pakistan e-mail: fs1005,saleemiqbal81,[email protected]. ABSTRACT: The fractional Fourier transform (FRFT) is a generalization of the ordinary Fourier transform (FT). Recently...

In this paper, the sampling theorem for bandlimited functions over domains is generalized to one over ∏ domains. The generalized theorem is applicable to the experimental design model in which each factor has a different number of levels and enables us to estimate the parameters in the model by using Fourier transforms. Moreover, the relationship between the proposed sampling theorem and orthog...