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The Cauchy problem for degenerate parabolic equations in Gevrey classes

Kunihiko Kajitani, Masahiro Mikami (1998)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The Cauchy problem for one class of parabolic pseudodifferential systems with nonsmooth symbols.

Litovchenko, V.A. (2008)

Sibirskij Matematicheskij Zhurnal

The convergence estimates for Galerkin-wavelet solution of periodic pseudodifferential initial value problems.

Nguyen Minh Chuong, Bui Kien Cuong (2003)

International Journal of Mathematics and Mathematical Sciences

The density of the area integral in $ℝ_{+}^{n + 1}$

Richard F. Gundy, Martin L. Silverstein (1985)

Annales de l'institut Fourier

Let $u (x, y)$ be a harmonic function in the half-plane $R_{+}^{n + 1}$ , $n \geq 2$ . We define a family of functionals $D (u; r), - \infty > r > \infty$ , that are analogs of the family of local times associated to the process $u (x_{t}, y_{t})$ where $(x_{t}, y_{t})$ is Brownian motion in $R_{+}^{n + 1}$ . We show that $D (u) = {sup}_{r} D (u; r)$ is bounded in $L^{p}$ if and only if $u (x, y)$ belongs to $H^{p}$ , an equivalence already proved by Barlow and Yor for the supremum of the local times. Our proof relies on the theory of singular integrals due to Caldéron and Zygmund, rather than the stochastic calculus.

The Essential Spectrum of Elliptic Systems of Mixed Order.

Gerd Grubb, Giuseppe Geymonat (1977)

Mathematische Annalen

The Fast Fourier Transform and the Numerical Solution of One-Dimensional Boundary Integral Equations.

U. Lamp, K.-T. Schleicher, W. Wendland (1985)

Numerische Mathematik

The Fourier integral operators on Hardy spaces associated with Herz spaces

Lixia Liu, Bolin Ma, Sanyang Liu (2011)

Czechoslovak Mathematical Journal

In this paper, it is proved that the Fourier integral operators of order $m$ , with $- n < m \leq - (n - 1) / 2$ , are bounded from three kinds of Hardy spaces associated with Herz spaces to their corresponding Herz spaces.

The geometric optics for a class of hyperbolic second order operators with Hölder continuous coefficients with respect to time

Massimo Cicognani (1991)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The level crossing problem in semi-classical analysis I. The symmetric case

Yves Colin de Verdière (2003)

Annales de l’institut Fourier

We describe a microlocal normal form for a symmetric system of pseudo-differential equations whose principal symbol is a real symmetric matrix with a generic crossing of eigenvalues. We use it in order to give a precise description of the microlocal solutions.

The level crossing problem in semi-classical analysis. II. The Hermitian case

Yves Colin de Verdière (2004)

Annales de l’institut Fourier

This paper is the second part of the paper ``The level crossing problem in semi-classical analysis I. The symmetric case''(Annales de l'Institut Fourier in honor of Frédéric Pham). We consider here the case where the dispersion matrix is complex Hermitian.

The microlocal Landau-Zener formula

Yves Colin de Verdière, Maurice Lombardi, Joël Pollet (1999)

Annales de l'I.H.P. Physique théorique

The nonrelativistic limit for the Weyl quantized Hamlitonians and pseudo-differential operators.

Michihiro Nagase, Tomio Umeda (1992)

Forum mathematicum

The normal symbol on Riemannian manifolds.

Pflaum, Markus J. (1998)

The New York Journal of Mathematics [electronic only]

The Oblique Derivative Problem. I.

Bengt Winzell (1977)

Mathematische Annalen

The propagation of singularities for pseudo-differential operators with self-tangential characteristics

N. Dencker (1987/1988)

Séminaire Équations aux dérivées partielles (Polytechnique)

The signature package on Witt spaces

Pierre Albin, Éric Leichtnam, Rafe Mazzeo, Paolo Piazza (2012)

Annales scientifiques de l'École Normale Supérieure

In this paper we prove a variety of results about the signature operator on Witt spaces. First, we give a parametrix construction for the signature operator on any compact, oriented, stratified pseudomanifold $X$ which satisfies the Witt condition. This construction, which is inductive over the ‘depth’ of the singularity, is then used to show that the signature operator is essentially self-adjoint and has discrete spectrum of finite multiplicity, so that its index—the analytic signature of $X$ —is well-defined....

Currently displaying 1 – 20 of 34