The Kontorovich – Lebedev Integral Transforms and Their Inverses ∗
نویسنده
چکیده
The numerical evaluation of the transforms in the title, and their inverses, is considered, using a variety of decomposition, truncation, and quadrature methods. Extensive numerical testing is provided and an application given to the numerical evaluation of the kernel of a Fredholm integral equation of interest in mixed boundary value problems on wedge-shaped domains. AMS subject classification: 44A15, 65D30, 65R10.
منابع مشابه
Lp-BOUNDEDNESS OF THE GENERAL INDEX TRANSFORMS
Abstract We establish the boundedness properties in Lp for a class of integral transformations with respect to an index of hypergeometric functions. In particular, by using the RieszThorin interpolation theorem we get the corresponding results in Lp(R+), 1 ≤ p ≤ 2 for the Kontorovich-Lebedev, Mehler-Fock and Olevskii index transforms. An inversion theorem is proved for general index transformat...
متن کاملSupports of Functions and Integral Transforms
In this paper we apply a method of spectral theory of linear operators [10] to establish relations between the support of a function f on R with properties of its image Tf under a linear operator T : R → R. The classical approach uses analytic continuation of the image Tf into some complex domain (theorems of Paley-Wiener type [4, 5, 6, 7]), and therefore, could not apply to functions whose ima...
متن کاملOn the Lebedev transformation in Hardy's spaces
We establish the inverse Lebedev expansion with respect to parameters and arguments of the modified Bessel functions for an arbitrary function from Hardy’s space H2,A, A> 0. This gives another version of the Fourier-integral-type theorem for the Lebedev transform. The result is generalized for a weighted Hardy space Ĥ2,A ≡ Ĥ2((−A,A);|Γ(1+Rez+iτ)|2dτ), 0 < A < 1, of analytic functions f(z),z = R...
متن کاملInfinite integrals of Whittaker and Bessel functions with respect to their indices
We obtain several new closed-form expressions for the evaluation of a family of infinite-domain integrals of the Whittaker functions W , x and M , x and the modified Bessel functions I x and K x with respect to the index . The new family of definite integrals is useful in a variety of contexts in mathematical physics. In particular, the integral involving K x represents a new example of the Kon...
متن کاملChebyshev polynomial approximations for some hypergeometric systems
The hypergeometric type differential equations of the second order with polynomial coefficients and their systems are considered. The realization of the Lanczos Tau Method with minimal residue is proposed for the approximate solution of the second order differential equations with polynomial coefficients. The scheme of Tau method is extended for the systems of hypergeometric type differential e...
متن کامل