Polygône de Newton et $b$-fonctions pour les modules microdifférentiels

DOI10.24033/asens.1538zbMath0646.58021OpenAlexW187814641MaRDI QIDQ3790354

Yves Laurent

Publication date: 1987

Published in: Annales scientifiques de l'École normale supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_1987_4_20_3_391_0

zbMATH Keywords

microdifferential operatorb-functionshomogeneous Lagrangian submanifold

Mathematics Subject Classification ID

Differential complexes (58J10) Linear higher-order PDEs (35G05) Relations of PDEs on manifolds with hyperfunctions (58J15)

Related Items (30)

Pentes algébriques et pentes analytiques d'un -module ⋮ On the tropicalization of D-ideals ⋮ Blow up for a holonomic system ⋮ Differential equations with irregular singular points in dimension two ⋮ Slopes of hypergeometric systems of codimension one ⋮ An algorithm of computing \(b\)-functions ⋮ Cycles évanescents, spécialisation et \({\mathcal D}\)-modules. (Nearby cycles, specialization and \({\mathcal D}\)-modules.) ⋮ Algorithms for \(b\)-functions, restrictions, and algebraic local cohomology groups of \(D\)-modules ⋮ On irregular binomial \(D\)-modules ⋮ The \(b\)-function with respect to weights of hypergeometric ideals of codimension one ⋮ Characteristic cycles and Gevrey series solutions of \(A\)-hypergeometric systems ⋮ Monodromy conjecture for semi‐quasihomogeneous hypersurfaces ⋮ A boundedness theorem for nearby slopes of holonomic -modules ⋮ Irregularity of hypergeometric systems via slopes along coordinate subspaces ⋮ Topological boundary values and regular \(\mathcal D\)-modules ⋮ Algorithms for \(b\)-functions, induced systems, and algebraic local cohomology of \(D\)-modules ⋮ Algorithms for \(D\)-modules -- restriction, tensor product, localization, and local cohomology groups ⋮ \({\mathcal D}\)-modules and characters of semisimple Lie groups ⋮ Irregular hypergeometric \(\mathcal D\)-modules ⋮ Algebraic aspects of hypergeometric differential equations ⋮ The analytic standard fan of a \(\mathcal D\)-module ⋮ Singularities of the hypergeometric system associated with a monomial curve ⋮ Irregular hypergeometric systems associated with a singular monomial curve ⋮ Gevrey solutions of the irregular hypergeometric system associated with an affine monomial curve ⋮ Unnamed Item ⋮ Regular \(b\)-functions of \(D\)-modules ⋮ Unnamed Item ⋮ Irregular modified $A$-hypergeometric systems ⋮ La transformation de Fourier pour les \({\mathcal D}\)-modules. (Fourier transform for \({\mathcal D}\)-modules) ⋮ Vanishing cycles of \(D\)-modules

Cites Work

• Systems of microdifferential equations. Notes and transl. by Teresa Monteiro Fernandes. Introd. by Jean-Luc Brylinski
• Formal and convergent solutions of singular partial differential equations
• Sur les points singuliers des équations différentielles
• On the maximally overdetermined system of linear differential equations. I
• B-functions and holonomic systems. Rationality of roots of B-functions
• Systems of differential equations with regular singularities and their boundary value problems
• Problème de Cauchy pour les systèmes microdifferentiels dans le domaine complexe
• On the holonomic systems of linear differential equations. II
• On holonomic systems of microdifferential equations. III: Systems with regular singularities
• Théorie de la deuxième microlocalisation dans le domaine complexe
• Pseudo-differential operators and Gevrey classes
• Théorèmes d’indices Gevrey pour les équations différentielles ordinaires
• The Integrability of the Characteristic Variety
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