An integral formula forL2-eigenfunctions of a fourth-order Bessel-type differential operator
نویسندگان
چکیده
منابع مشابه
Fourth-order Bessel-type Special Functions: a Survey
This survey paper reports on the properties of the fourth-order Bessel-type linear ordinary differential equation, on the generated self-adjoint differential operators in two associated Hilbert function spaces, and on the generalisation of the classical Hankel integral transform. These results are based upon the properties of the classical Bessel and Laguerre second-order differential equations...
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 کاملBeta Type Integral Formula Associated with Wright Generalized Bessel Function
Abstract. The object of the present paper is to establish an integral formula involving Wright generalized Bessel function (or generalized Bessel-Maitland function) J ν,q (z) defined by Singh et al. [21], which is expressed in the terms of generalized (Wright) hypergeometric functions. Some interesting special cases involving Bessel functions, generalized Bessel functions, generalized Mittag-Le...
متن کاملOn the Solvability of a Fourth Order Operator Differential Equations
We establish sufficient conditions for the solvability of a fourth order operator differential equation. These conditions are expressed in terms of operator coefficients. 1. Preliminaries In this paper we consider the problem P (d/dt)u = du dt4 +Au+ 4 ∑ j=0 Aj d4−ju dt4−j = f, (1.1) e1 ui(0) = 0, i = 0, 1, si ∈ {0, 1, 2, 3}, (1.2) e2 where f ∈ L2(R+,H), and A0, A1, A2, A3, A4 and A are unbounde...
متن کاملSome Properties of an Integral Operator Defined by Bessel Functions
In this paper we will study the integral operator involving Bessel functions of the first kind and of order v.We will investigate the integral operator for the classes of starlike and convex functions in the open unit disk.
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: Integral Transforms and Special Functions
سال: 2011
ISSN: 1065-2469,1476-8291
DOI: 10.1080/10652469.2010.533270