Teachers:\u00a0Philippe Jaming and Bernhard Haak<\/p>\n\n\n\n
The aim of this course is to provide analytical tools for the study of partial differential equations (PDEs). The course is split in two parts that are run simultaneously.<\/p>\n\n\n\n
\u2013 In the first part, we introduce the main tools of harmonic analysis to study the class of singular integral operators.<\/p>\n\n\n\n
\u2013 In the second part, we give and introduction introduce semigroup theory.<\/p>\n\n\n\n
Harmonic Analysis (Ph. Jaming) \u2013 $L^p$ and weak $L^p$ spaces, interpolation. \u2013 Fourier analysis, Sobolev spaces, Paley-Wiener spaces. \u2013 Hardy-Littlewood maximal function: covering lemma, boundedness of the maximal function, application to Lebesgue differentiation theorem. Harmonic functions on the half-space, Poisson kernel and boundary behavior. \u2013 Hilbert and Riesz transforms. \u2013 Singular integrals, Calderon-Zygmund decomposition. \u2013 BMO (bounded mean oscillation). \u2013 Littlewood-Paley multiplier theorem and H\u00f6rmander multiplier theorem.<\/p>\n\n\n\n
Introduction to semigroups (B. Haak) \u2013 semigroups and their generators for solving the abstract Cauchy problem: uniformly continuous and strong continuous semigroups, generation theorems (Hille-Yosida and Lumer-Philipps), analytic semigroups, regularity of solutions. At the end of the course we discuss maximal regularity as a tool to solve non-linear equations by fixed point methods. This requires tools from harmonic analysis developed in the first part.<\/p>\n","protected":false},"excerpt":{"rendered":"
Teachers:\u00a0Philippe Jaming and Bernhard Haak The aim of this course is to provide analytical tools for the study of partial differential equations (PDEs). The course is split in two parts that are run simultaneously. \u2013 In the first part, we introduce the main tools of harmonic analysis to study the class of singular integral operators. … Continue reading “Advanced course in analysis”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":4,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-461","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages\/461","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/comments?post=461"}],"version-history":[{"count":4,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages\/461\/revisions"}],"predecessor-version":[{"id":564,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages\/461\/revisions\/564"}],"up":[{"embeddable":true,"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/pages\/4"}],"wp:attachment":[{"href":"https:\/\/uf-mi.u-bordeaux.fr\/algant\/index.php\/wp-json\/wp\/v2\/media?parent=461"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}