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Sequence spaces with exponent weights. Realizations of Colombeau type algebras

100%
Delcroix A., Hasler M., Pilipović S., Valmorin V.
Instytut Matematyczny Polskiej Akademii Nauk
EN
We give a description of various algebras of generalized functions based on the introduction of pseudo-ultranorms on spaces of sequences in given locally convex function algebras. We study sheaf properties of these algebras, needed for microlocal analysis, and also consider regularity theory, functoriality and different concepts of association and weak equality in a unified setting. Using this approach, we also give new results on embeddings of ultradistribution and hyperfunction spaces into corresponding algebras of generalized functions.
2
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Hilbert transform and singular integrals on the spaces of tempered ultradistributions

91%
Kamiński A., Perišić D., Pilipović S.
Banach Center Publications
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2000
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tom 53
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nr 1
139-153
EN
The Hilbert transform on the spaces $S'*(R^d)$ of tempered ultradistributions is defined, uniquely in the sense of hyperfunctions, as the composition of the classical Hilbert transform with the operators of multiplying and dividing a function by a certain elliptic ultrapolynomial. We show that the Hilbert transform of tempered ultradistributions defined in this way preserves important properties of the classical Hilbert transform. We also give definitions and prove properties of singular integral operators with odd and even kernels on the spaces $S'*(R^d)$, whose special cases are the Hilbert transform and Riesz operators.
3
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Classes of distribution semigroups

91%
Kunstmann P., Mijatović M., Pilipović S.
Studia Mathematica
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2008
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tom 187
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nr 1
37-58
EN
We introduce various classes of distribution semigroups distinguished by their behavior at the origin. We relate them to quasi-distribution semigroups and integrated semigroups. A class of such semigroups, called strong distribution semigroups, is characterized through the value at the origin in the sense of Łojasiewicz. It contains smooth distribution semigroups as a subclass. Moreover, the analysis of the behavior at the origin involves intrinsic structural results for semigroups. To this purpose, new test function spaces and distribution semigroups over these spaces are introduced. We give applications to Schrödinger type equations in the spaces $C_{b}$, $L^{∞}$, and BMO with elliptic non-densely defined operators.
4
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On regular $K'{M_P}$-distributions

79%
Pilipović S.
Annales Polonici Mathematici
|
1988
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tom 48
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nr 1
31-39
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