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1
Content available remote

Generalized analytic functions of Bogdan Ziemian

100%
Łysik G.
Annales Polonici Mathematici
|
2000
|
tom 74
|
nr 1
35-41
EN
Definitions, properties, examples and applications of generalized analytic functions introduced by B. Ziemian are presented.
2
Content available remote

Laplace ultradistributions on a half line and a strong quasi-analyticity principle

100%
Łysik G.
Annales Polonici Mathematici
|
1996
|
tom 63
|
nr 1
13-33
EN
Several representations of the space of Laplace ultradistributions supported by a half line are given. A strong version of the quasi-analyticity principle of Phragmén-Lindelöf type is derived.
3
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The Taylor transformation of analytic functionals with non-bounded carrier

100%
Łysik G.
Studia Mathematica
|
1994
|
tom 108
|
nr 2
159-176
EN
Let L be a closed convex subset of some proper cone in ℂ. The image of the space of analytic functionals Q'(L) with non-bounded carrier in L under the Taylor transformation as well as the representation of analytic functionals from Q'(L) as the boundary values of holomorphic functions outside L are given. Multipliers and operators in Q'(L) are described.
4
Content available remote

A Phragmén-Lindelöf type quasi-analyticity principle

100%
Łysik G.
Studia Mathematica
|
1997
|
tom 123
|
nr 3
217-234
EN
Quasi-analyticity theorems of Phragmén-Lindelöf type for holomorphic functions of exponential type on a half plane are stated and proved. Spaces of Laplace distributions (ultradistributions) on ℝ are studied and their boundary value representation is given. A generalization of the Painlevé theorem is proved.
5
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Borel summable solutions of the Burgers equation

100%
Łysik G.
Annales Polonici Mathematici
|
2009
|
tom 95
|
nr 2
187-197
EN
We give necessary and sufficient conditions for the formal power series solutions to the initial value problem for the Burgers equation $∂_t u -∂_x² u = ∂_x(u²)$ to be convergent or Borel summable.
6
Content available remote

Laplace integrals in partial differential equations in papers of Bogdan Ziemian

100%
Łysik G.
Annales Polonici Mathematici
|
2000
|
tom 74
|
nr 1
43-50
EN
Fundamental solutions to linear partial differential equations with constant coefficients are represented in the form of Laplace type integrals.
7
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Nonanalyticity of solutions to $∂_{t}u = ∂²_{x}u + u²$

100%
Łysik G.
Colloquium Mathematicum
|
2003
|
tom 95
|
nr 2
255-266
EN
It is proved that the solution to the initial value problem $∂_{t}u = ∂²_{x}u + u²$, u(0,x) = 1/(1+x²), does not belong to the Gevrey class $G^s$ in time for 0 ≤ s < 1. The proof is based on an estimation of a double sum of products of binomial coefficients.
8
Content available remote

On 1-regular ordinary differential operators

100%
Łysik G.
Annales Polonici Mathematici
|
2000
|
tom 74
|
nr 1
201-214
EN
Solutions to singular linear ordinary differential equations with analytic coefficients are found in the form of Laplace type integrals.
9
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Uniform analytic-Gevrey regularity of solutions to a semilinear heat equation

64%
Gramchev T., Łysik G.
Banach Center Publications
|
2008
|
tom 81
|
nr 1
213-226
EN
We study the Gevrey regularity down to t = 0 of solutions to the initial value problem for a semilinear heat equation $∂_tu - Δu = u^M$. The approach is based on suitable iterative fixed point methods in $L^p$ based Banach spaces with anisotropic Gevrey norms with respect to the time and the space variables. We also construct explicit solutions uniformly analytic in t ≥ 0 and x ∈ ℝⁿ for some conservative nonlinear terms with symmetries.
10
Content available remote

A characterization of elliptic operators

64%
Łysik G., Wójcicki P.
Annales Polonici Mathematici
|
2014
|
tom 111
|
nr 2
145-148
EN
We give a characterization of constant coefficients elliptic operators in terms of estimates of their iterations on smooth functions.
11
Content available remote

Bogdan Ziemian (1953-1997)

52%
Bojarski B., Łojasiewicz S., Łysik G., Szmydt Z.
Annales Polonici Mathematici
|
2000
|
tom 74
|
nr 1
1-11
12
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On the structure of Mellin distributions

38%
Łysik G.
Annales Polonici Mathematici
|
1990
|
tom 51
|
nr 1
219-228
13
Content available remote

Generalized Taylor expansions of singular functions

32%
Łysik G.
Studia Mathematica
|
1991
|
tom 99
|
nr 3
235-262
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