Open AccessINTEGRAL TRANSFORM WITH THE EXTENDED GENERALIZED MITTAG‐LEFFLER FUNCTION
Author(s) -
Anatoly A. Kilbas,
Anna A. Koroleva
Publication year - 2006
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2006.9637311
Subject(s) - mathematics , integral transform , mellin transform , fractional fourier transform , pure mathematics , representation (politics) , radon transform , lebesgue integration , function (biology) , mathematical analysis , inversion (geology) , two sided laplace transform , laplace transform , fourier transform , fourier analysis , paleontology , structural basin , evolutionary biology , politics , political science , law , biology
he paper is devoted to the study of the integral transformcontaining the special function å((á, â) n ;z) generalizing the Mittag‐Leffler type function in the space £v,r (1 ≤ r ≤ 8, í ∈ R) of Lebesgue measurable functions on R+ = (0,+8) such that ‖ƒ‖ v,r < 8, whereMapping properties such as the boundedness, the range, the representation and the inversion of the considered transform are proved. The results are based on the representation of the considered transform as the H‐transform.