Gaussian measures on $L_p$ spaces, $0\le p < \infty $

Byczkowski, Tomasz

Displaying similar documents to “Gaussian measures on $L_{p}$ spaces, $0 \leq p < \infty$ ”

Spaces of type $H^{\infty} + C$

Walter Rudin (1975)

Annales de l'institut Fourier

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A simple theorem is proved which states a sufficient condition for the sum ot two closed subspaces of a Banach space to be closed. This leads to several analogues of Sarason’s theorem which states that $H^{\infty} + C$ is a closed subalgebra of $L^{\infty}$ . In these analogues, the unit circle is replaces by other groups, and the unit disc is replaced by polydiscs or by balls in spaces of several complex variables. Sums of closed ideals in Banach algebras are also studied.

The partial Malliavin calculus

David Nualart, Moshe Zakai (1989)

Séminaire de probabilités de Strasbourg

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Propagation of singularities for the wave equation on manifolds with corners

András Vasy (2004-2005)

Séminaire Équations aux dérivées partielles

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In this talk we describe the propagation of $𝒞^{\infty}$ and Sobolev singularities for the wave equation on $𝒞^{\infty}$ manifolds with corners $M$ equipped with a Riemannian metric $g$ . That is, for $X = M \times ℝ_{t}$ , $P = D_{t}^{2} - Δ_{M}$ , and $u \in H_{loc}^{1} (X)$ solving $P u = 0$ with homogeneous Dirichlet or Neumann boundary conditions, we show that ${WF}_{b} (u)$ is a union of maximally extended generalized broken bicharacteristics. This result is a $𝒞^{\infty}$ counterpart of Lebeau’s results for the propagation of analytic singularities on real analytic manifolds with appropriately stratified...