scholarly journals Computation of Fourier transform representations involving the generalized Bessel matrix polynomials

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. Abdalla ◽  
M. Akel
Keyword(s):  
Fourier Transform ◽  
Orthogonal Polynomials ◽  
Integral Transforms ◽  
General Character ◽  
Matrix Functions ◽  
Fourier Cosine ◽  
Matrix Polynomials ◽  
The Matrix ◽  
Special Matrix ◽  
Special Matrix Functions

AbstractMotivated by the recent studies and developments of the integral transforms with various special matrix functions, including the matrix orthogonal polynomials as kernels, in this article we derive the formulas for Fourier cosine and sine transforms of matrix functions involving generalized Bessel matrix polynomials. With the help of these transforms several results are obtained, which are extensions of the corresponding results in the standard cases. The results given here are of general character and can yield a number of (known and new) results in modern integral transforms.

Computation of Fourier transform representations involving the generalized Bessel matrix polynomials

2021 ◽  
Author(s):  
mohamed abdalla
Keyword(s):  
Fourier Transform ◽  
Orthogonal Polynomials ◽  
Integral Transforms ◽  
General Character ◽  
Matrix Functions ◽  
Fourier Cosine ◽  
Matrix Polynomials ◽  
The Matrix ◽  
Special Matrix ◽  
Special Matrix Functions

Abstract Motivated by the recent studies and developments of the integral transforms with various special matrix functions, including the matrix orthogonal polynomials as kernels. In this article, we derive the formulas for Fourier cosine transforms and Fourier sine transforms of matrix functions involving generalized Bessel matrix polynomials. With the help of these transforms a number of results are considered which are extensions of the corresponding results in the standard cases. The results given here are of general character and can yield a number of (known and new) results in modern integral transforms.

scholarly journals Generalizations of two-index two-variable Hermite matrix polynomials

2009 ◽  
Vol 42 (4) ◽  
Author(s):  
M. S. Metwally ◽  
M. T. Mohamed ◽  
A. Shehata
Keyword(s):  
Wide Class ◽  
Recurrence Formula ◽  
Explicit Representation ◽  
Matrix Exponential ◽  
Matrix Functions ◽  
Differential Systems ◽  
Matrix Polynomials ◽  
The Matrix ◽  
Hermite Matrix ◽  
Class Of Matrices

AbstractIn this paper, we introduce a new generalization of the Hermite matrix polynomials expansions of some relevant matrix functions appearing in the solution of differential systems. An explicit representation and an expansion of the matrix exponential in a series of these matrix polynomials is obtained. Properties of Hermite matrix polynomials such as the recurrence formula permit an efficient computations of matrix functions are established. A new expansions of the matrix exponential for a wide class of matrices in terms of Hermite matrix polynomials is proposed.

ON q-EXTENSIONS OF MEHTA'S EIGENVECTORS OF THE FINITE FOURIER TRANSFORM

2006 ◽  
Vol 21 (23n24) ◽  
pp. 4993-5006 ◽  
Author(s):  
NATIG M. ATAKISHIYEV
Keyword(s):  
Fourier Transform ◽  
Hermite Polynomials ◽  
Integral Transforms ◽  
Fourier Integral ◽  
Hermite Functions ◽  
Continuous Limit ◽  
Finite Fourier Transform ◽  
The Matrix ◽  
Matrix Formula

Mehta has shown that eigenvectors [Formula: see text] of the finite Fourier transform with the matrix [Formula: see text], 0 ≤ j, k ≤ N-1, can be defined in terms of the classical Hermite functions [Formula: see text] as [Formula: see text], where [Formula: see text]. We argue that the finite Fourier transform [Formula: see text] does actually govern also some q-extensions of Mehta's eigenvectors [Formula: see text], associated with certain well-known orthogonal q-polynomial families. For the pairs of the continuous q-Hermite and q-1-Hermite polynomials, the Rogers–Szegő and Stieltjes–Wigert polynomials, and the discrete q-Hermite polynomials of types I and II such links are explicitly derived. In the limit when the base q → 1 these q-extensions coincide with Mehta's eigenvectors [Formula: see text], whereas in the continuous limit (i.e. when the parameter N → ∞) they correspond to the classical Fourier integral transforms between the above-mentioned pairs of q-polynomial families.

New kind of special matrix functions and generating functions

2018 ◽  
Vol 11 (02) ◽  
pp. 1850028
Author(s):  
Ahmed Ali Al-Gonah ◽  
Fatima Mohammed Al-Samadi
Keyword(s):  
Generating Functions ◽  
Matrix Function ◽  
Laguerre Polynomials ◽  
Matrix Functions ◽  
Hermite Matrix ◽  
Special Matrix ◽  
Operational Methods ◽  
Special Matrix Functions

In this paper, a new kind of special matrix functions is introduced and some properties of these special matrix function are established. Further, some generating functions for the 3-variable Hermite matrix-based Laguerre polynomials involving the special matrix function are derived by using operational methods.

scholarly journals Analytical Properties of the Generalized Heat Matrix Polynomials Associated with Fractional Calculus

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Mohamed Abdalla ◽  
Salah Mahmoud Boulaaras
Keyword(s):  
Fractional Calculus ◽  
Integral Transforms ◽  
Matrix Functions ◽  
Matrix Polynomials ◽  
Matrix Version ◽  
Analytical Properties ◽  
Fractional Calculus Operators ◽  
Finite Sums ◽  
Generating Matrix Functions ◽  
Generating Matrix

In this paper, we introduce a matrix version of the generalized heat polynomials. Some analytic properties of the generalized heat matrix polynomials are obtained including generating matrix functions, finite sums, and Laplace integral transforms. In addition, further properties are investigated using fractional calculus operators.

scholarly journals The Nevanlinna parametrization for a matrix moment problem

2001 ◽  
Vol 89 (2) ◽  
pp. 245 ◽  
Author(s):  
Pedro Lopez-Rodriguez
Keyword(s):  
Half Plane ◽  
Moment Problem ◽  
Matrix Function ◽  
Unitary Matrix ◽  
Matrix Functions ◽  
Matrix Polynomials ◽  
Analytic Matrix ◽  
The Matrix ◽  
Upper Half Plane ◽  
Matrix Moment

We obtain the Nevanlinna parametrization for an indeterminate matrix moment problem, giving a homeomorphism between the set $V$ of solutions to the matrix moment problem and the set $\mathcal V$ of analytic matrix functions in the upper half plane such that $V(\lambda )^*V(\lambda )\le I$. We characterize the N-extremal matrices of measures (those for which the space of matrix polynomials is dense in their $L^2$-space) as those whose corresponding matrix function $V(\lambda )$ is a constant unitary matrix.

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