Second-Order Differential Operators Having Several Families of Orthogonal Matrix Polynomials as Eigenfunctions
نویسندگان
چکیده
منابع مشابه
Second order differential operators having several families of orthogonal matrix polynomials as eigenfunctions
The aim of this paper is to bring into the picture a new phenomenon in the theory of orthogonal matrix polynomials satisfying second order differential equations. The last few years have witnessed some examples of a (fixed) family of orthogonal matrix polynomials whose elements are common eigenfunctions of several linearly independent second order differential operators. We show that the dual s...
متن کاملSome examples of matrix-valued orthogonal functions having a differential and an integral operator as eigenfunctions
The aim of this paper is to show some examples of matrix-valued orthogonal functions on the real line which are simultaneously eigenfunctions of a second-order differential operator of Schrödinger type and an integral operator of Fourier type. As a consequence we derive integral representations of these functions as well as other useful structural formulas. Some of these functions are plotted t...
متن کاملOrthogonal matrix polynomials satisfying second order difference equations
We develop a method that allows us to construct families of orthogonal matrix polynomials of size N ×N satisfying second order difference equations with polynomial coefficients. The existence (and properties) of these orthogonal families strongly depends on the non commutativity of the matrix product, the existence of singular matrices and the matrix size N .
متن کاملOrthogonal Polynomial Eigenfunctions of Second-order Partial Differerential Equations
In this paper, we show that for several second-order partial differential equations L[u] = A(x, y)uxx + 2B(x, y)uxy + C(x, y)uyy +D(x, y)ux + E(x, y)uy = λnu which have orthogonal polynomial eigenfunctions, these polynomials can be expressed as a product of two classical orthogonal polynomials in one variable. This is important since, otherwise, it is very difficult to explicitly find formulas ...
متن کاملUsing DD-operators to construct orthogonal polynomials satisfying higher order difference or differential equations
We introduce the concept of D-operators associated to a sequence of polynomials (pn)n and an algebra A of operators acting in the linear space of polynomials. In this paper, we show that this concept is a powerful tool to generate families of orthogonal polynomials which are eigenfunctions of a higher order difference or differential operator. Indeed, given a classical discrete family (pn)n of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2008
ISSN: 1687-0247,1073-7928
DOI: 10.1093/imrn/rnn084