Grzegorz Łysik, Associate Professor

Ph.D.: 1989 IM PAN, habilitation: 2000 IM PAN

My field of interest is the analysis of generalized analytic functions, i. e. holomorphic functions with branch singularities. Such functions near isolated singular point (say 0) have a "continuous" Taylor type expansion into powers xa, a in R with some density being a generalized function. They are closely related to resurgent functions of J. Ecalle. They behave well under algebraic and differential operations and appear as solutions to singular differential equations both linear and non-linear. In my research I mainly use methods of complex analysis and the theory of ultradistributions and hyperfunctions. As my main achievement I consider a modification of the Mellin transformation in a way suitable for the study of generalized analytic functions with exponential growth at zero. Another is derivation of new versions of quasi-analyticity principle for functions holomorphic in a half plane.

Selected publications
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