Convolution for the mehler–fock transform of generalized functions

References

• Dieudonné , J. 1974 . Elements d'Analyse , Vol. 2 , Paris : Gauthier-Villars . Second edition
   Google Scholar
• Erdelyi , A. , Magnus , W. , Oberhettinger , F. and Tricomi , F.G. 1953 . Higher Transcendental Functions , Vol. I , New York : McGraw-Hill .
   Google Scholar
• Fock , V. 1943 . On the representation of an arbitrary function by an integral involving Legendre's function with a complex index . Dokl. Akad. Nauk. SSSR , 39 : 279 – 283 .
   Google Scholar
• Gasper , G. 1971 . Positivity and the convolution structure for Jacobi series . Ann. of Math. , 93 : 112 – 118 .
   Web of Science ®Google Scholar
• Glaeske , H.-J. and Hess , A. 1987 . On the convolution theorem of the Mehler–Fock transform for a class of generalized functions (I) . Math. Nachr. , 131 : 107 – 117 .
   Google Scholar
• Glaeske , H.-J. and Hess , A. 1988 . On the convolution theorem of the Mehler–Fock transform for a class of generalized functions (II) . Math. Nachr. , 136 : 119 – 129 .
   Google Scholar
• González , B.J. and Negrin , E.R. 1997 . Mehler–Fock transforms of generalized functions via the method of adijoints . Proc. Amer. Math. Soc. , 125 : 3243 – 3253 .
   Web of Science ®Google Scholar
• Hayek , N. and González , B.J. 1992 . On the Mehler–Fock transform of generalized functions . Bull. Soc. Roy. Sci. Liëge , 61 : 315 – 327 .
   Google Scholar
• Hayek , N. and González , B.J. 1993 . A convolution theorem for the index 2 F 1-transform . J. Inst. Math. Comp. Sci. Math. Ser. , 6 : 21 – 24 .
   Google Scholar
• Henrici , P. 1955 . Addition theorems for general Legendre and Gegenbauer functions . J. Rat. Mech. Anal. , 4 : 983 – 1018 .
   Google Scholar
• Olver , F.W.J. 1997 . Asymptotics and Special Functions , New York : Academic Press .
   Google Scholar
• Rosenthal , P. 1974 . On the inversion theorem for the general Mehler–Fock transform pair . Pacific J. Math. , 52 : 539 – 545 .
   Google Scholar
• Sneddon , I.N. 1972 . The Use of Integral Transforms , New York : McGraw-Hill .
   Google Scholar
• Srivastava , H.M. and Tuan , V.K. 1995 . A new convolution theorem for the Stieltjes transform and its application to a class of sigular integral equations . Arch. Math. , 64 : 144 – 149 .
   Web of Science ®Google Scholar
• Tiwari , U.N. and Pandey , J.N. 1980 . The Mehler–Fock transform of distributions . Rocky Mountain J. Math. , 10 : 401 – 408 .
   Google Scholar
• Yakubovich , S.B. 1996 . Index Transforms , Singapore : World Scientific Publishing Company . (With a Foreword by H.M. Srivastava)
   Google Scholar
• Yakubovich , S.B. and Saigo , M. 1997 . On the Mehler–Fock transform in Lp-space . Math. Nachr. , 185 : 261 – 277 .
   Web of Science ®Google Scholar