## 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 *x*^{a},
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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