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Sharp estimates of the Jacobi heat kernel

Adam Nowak ; Peter Sjögren (Institutionen för matematiska vetenskaper, matematik)
Studia Mathematica (0039-3223). Vol. 218 (2013), 3, p. 219-244.
[Artikel, refereegranskad vetenskaplig]

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 two other classical systems of orthogonal polynomials. We deduce sharp estimates giving the order of magnitude of this kernel, for type parameters above -1/2. As an application of the upper bound obtained, 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.

Nyckelord: Jacobi polynomial; Jacobi expansion; Jacobi heat kernel; Poisson-Jacobi kernel; Jacobi semigroup; maximal operator



Denna post skapades 2011-11-22. Senast ändrad 2016-11-07.
CPL Pubid: 148827

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematisk analys

Chalmers infrastruktur