Functional Analysis and Applications Seminar 

19/07/2002, 14:00 — 15:00 — Room P3.10, Mathematics Building
Semyon Yakubovich, Universidade do Porto

Recent Results on Some Integral Operators Associated with theKontorovich-Lebedev Transformation

Further developments of the results on the Kontorovich-Lebedev type transformations and associated convolution in $L_p$ spaces are given. In particular, we consider compositions with the Mellin type convolution transformations and obtain some interesting cases of integral transforms depending upon parameters of hypergeometric functions (the Lommel functions, the Whittaker functions, the Clausenian functions, etc.). Boundedness properties are investigated, Plancherel type theorems are proved. Parseval type identities are established. Applications to integral equations of the Fredholm and convolution type associated with the Kontorovich-Lebedev operator are given.