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Abstrakty
The heat kernel associated with the setting of the classical Jacobi polynomials is defined by an oscillatory sum which cannot be computed explicitly, in contrast to the situation for the other two classical systems of orthogonal polynomials. We deduce sharp estimates giving the order of magnitude of this kernel, for type parameters α, β ≥ -1/2. Using quite different methods, Coulhon, Kerkyacharian and Petrushev recently also obtained such estimates. As an application of the bounds, we show that the maximal operator of the multi-dimensional Jacobi heat semigroup satisfies a weak type (1,1) inequality. We also obtain sharp estimates of the Poisson-Jacobi kernel.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
219-244
Opis fizyczny
Daty
wydano
2013
Twórcy
autor
- Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland
autor
- Mathematical Sciences, University of Gothenburg
- Mathematical Sciences, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
Bibliografia
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Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm218-3-2