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Quelques espaces fonctionnels associés à des processus gaussiens

100%

Ciesielski Z., Kerkyacharian G., Roynette B.

Studia Mathematica

1993

tom 107

nr 2

171-204

The first part of the paper presents results on Gaussian measures supported by general Banach sequence spaces and by particular spaces of Besov-Orlicz type. In the second part, a new constructive isomorphism between the just mentioned sequence spaces and corresponding function spaces is established. Consequently, some results on the support function spaces for the Gaussian measure corresponding to the fractional Brownian motion are proved. Next, an application to stochastic equations is given. The last part of the paper contains a result on the support function spaces for stable processes with independent increments.

Compactly supported frames for spaces of distributions associated with nonnegative self-adjoint operators

100%

Dekel S., Kerkyacharian G., Kyriazis G., Petrushev P.

Studia Mathematica

2014

tom 225

nr 2

115-163

A small perturbation method is developed and employed to construct frames with compactly supported elements of small shrinking support for Besov and Triebel-Lizorkin spaces in the general setting of a doubling metric measure space in the presence of a nonnegative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. This allows one, in particular, to construct compactly supported frames for Besov and Triebel-Lizorkin spaces on the sphere, on the interval with Jacobi weights as well as on Lie groups, Riemannian manifolds, and in various other settings. The compactly supported frames are utilized to introduce atomic Hardy spaces $H^{p}_{A}$ in the general setting of this article.

Ograniczanie wyników

2 Studia Mathematica

2 Kerkyacharian G.

1 Ciesielski Z.

1 Dekel S.

1 Kyriazis G.

1 Petrushev P.

1 Roynette B.

1 2014

1 1993

Wyniki wyszukiwania

Quelques espaces fonctionnels associés à des processus gaussiens

Compactly supported frames for spaces of distributions associated with nonnegative self-adjoint operators