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Notes on integral transformations

100%
Szeptycki P.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS 1. Introduction...............................................................................5 2. Spaces of measurable functions...............................................7 3. Proper domain of an integral transformation...........................14 4. Integral transformations in L⁰. Continuity and closibility...........17 5. Extensions by continuity. Compatibility problem.......................21 6. Compactness of integral transformations................................35 7. Miscellaneous results and comments......................................41 8. Bibliographical remarks and comments...................................46 Bibliography.................................................................................48
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Integration of polynomials

96%
Szeptycki P.
Applicationes Mathematicae
|
2004
|
tom 31
|
nr 1
1-4
EN
We prove that the only functions for which certain standard numerical integration formulas are exact are polynomials.
3
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Locally convex domains of integral operators

96%
Szeptycki P.
Banach Center Publications
|
2005
|
tom 67
|
nr 1
357-361
EN
We have shown in [1] that domains of integral operators are not in general locally convex. In the case when such a domain is locally convex we show that it is an inductive limit of L¹-spaces with weights.
4
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Domains of integral operators

61%
Labuda I., Szeptycki P.
Studia Mathematica
|
1994
|
tom 111
|
nr 1
53-68
EN
It is shown that the proper domains of integral operators have separating duals but in general they are not locally convex. Banach function spaces which can occur as proper domains are characterized. Some known and some new results are given, illustrating the usefulness of the notion of proper domain.
5
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$L^{2}$ and $L^{p}$ estimates for oscillatory integrals and their extended domains

49%
Pan Y., Sampson G., Szeptycki P.
Studia Mathematica
|
1997
|
tom 122
|
nr 3
201-224
EN
We prove the $L^p$ boundedness of certain nonconvolutional oscillatory integral operators and give explicit description of their extended domains. The class of phase functions considered here includes the function $|x|^{α}|y|^{β}$. Sharp boundedness results are obtained in terms of α, β, and rate of decay of the kernel at infinity.
6
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Extensions by mollifiers in Basov spaces

31%
Szeptycki P.
Studia Mathematica
|
1975-1976
|
tom 54
|
nr 1
55-72
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