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This work is devoted to a systematic study of the microlocal regularity properties of pseudo-differential operators with the transmission property. We introduce a “boundary singular spectrum”, denoted $\partial W F_{ω} (u)$ for distributions $u \in D^{'} (R_{+}^{n})$ , regular in the normal variable $x_{n}$ (thus, $\partial W F_{ω} (u) = \emptyset$ means that $u \in \cap_{s + t = 1 / 2} H^{s + t}$ near the boundary), and it is shown that $\partial W F_{ω - m} [P (u^{0})_{x_{n} > 0}]$ is a subset of $\partial W F (u)$ if $P$ has degree $m$ and the transmission property. We finally prove that these results can bef used to examinate the (microlocal) regularity of the solutions of differential...

Microlocal solvability of the Cauchy problem and boundary regularity

Otto Liess (1987)

Banach Center Publications

Microlocal structure of a single linear pseudodifferential equation

M. Sato (1972/1973)

Séminaire Équations aux dérivées partielles (Polytechnique)

Microlocal tempered inverse image and Cauchy problem.

Tonin, F. (1999)

Portugaliae Mathematica

Microlocal time decays for hyperbolic eqations with lower order terms.

Ruzhansky, Michael (2008)

Novi Sad Journal of Mathematics

Microlocalisation et estimations pour ... Dans quelques hypersurfaces pseudoconvexes.

Makhlouf Derridj (1991)

Inventiones mathematicae

Microlocalisation et estimations pour ${\bar{\partial}}_{b}$

M. Derridj (1990/1991)

Séminaire Équations aux dérivées partielles (Polytechnique)

Microlocalisation hypo-analytique et extension holomorphe de fonctions C. R.

M. S. Baouendi (1981/1982)

Séminaire Équations aux dérivées partielles (Polytechnique)

Microlocalisation simultanée et problème de Cauchy ramifié

Jean-Marc Delort (1996)

Compositio Mathematica

Microlocalisation simultanée et problème de Cauchy ramifié

J.-M. Delort (1992/1993)

Séminaire Équations aux dérivées partielles (Polytechnique)

Microlocalisation tempérée. Application aux distributions holonomes sur une variété complexe

E. Andronikof (1987/1988)

Séminaire Équations aux dérivées partielles (Polytechnique)

Microlocalization of resonant states and estimates of the residue of the scattering amplitude

Jean-François Bony, Laurent Michel (2003)

Journées équations aux dérivées partielles

We obtain some microlocal estimates of the resonant states associated to a resonance $z_{0}$ of an $h$ -differential operator. More precisely, we show that the normalized resonant states are $𝒪 (\sqrt{| Im z_{0} | / h}$ $+ h^{\infty} ...$

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Microlocal analysis in the dual of a Colombeau algebra: generalized wave front sets and noncharacteristic regularity.

Microlocal boundary value problem in higher codimensions

Microlocal operators with plurisubharmonic growth

Microlocal properties of a class of pseudodifferential operators with double involutive characteristics

Microlocal regularity at the boundary for pseudo-differential operators with the transmission property (I)

Microlocal solvability of the Cauchy problem and boundary regularity

Microlocal structure of a single linear pseudodifferential equation

Microlocal tempered inverse image and Cauchy problem.

Microlocal time decays for hyperbolic eqations with lower order terms.

Microlocalisation et estimations pour ... Dans quelques hypersurfaces pseudoconvexes.

Microlocalisation et estimations pour ${\bar{\partial}}_{b}$

Microlocalisation hypo-analytique et extension holomorphe de fonctions C. R.

Microlocalisation simultanée et problème de Cauchy ramifié

Microlocalisation simultanée et problème de Cauchy ramifié

Microlocalisation tempérée. Application aux distributions holonomes sur une variété complexe

Microlocalization of resonant states and estimates of the residue of the scattering amplitude

Microscopic shocks in one dimensional driven systems

Microscopic structure of shocks in one conservation laws

Micro-support and Cauchy problem for temperate solutions of regular $𝒟$ -modules.

Milton's conjecture on the regularity of solutions to isotropic equations

Currently displaying 201 – 220 of 515