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This book presents original research results on pseudodifferential operators. C*-algebras generated by pseudodifferential operators with piecewise smooth symbols on a smooth manifold are considered. For each algebra, all the equivalence classes of irreducible representations are listed; as a consequence, a criterion for a pseudodifferential operator to be Fredholm is stated, the topology on the spectrum is described, and a solving series is constructed. Pseudodifferential operators on manifolds with edges are introduced, their properties are considered in details, and an algebra generated by the operators is studied. An introductory chapter includes all necessary preliminaries from the theory of pseudodifferential operators and C*-algebras.

Operator theory. --- Operator Theory. --- Functional analysis --- Pseudodifferential operators. --- Operators, Pseudodifferential --- Pseudo-differential operators --- Operator theory --- Operadors pseudodiferencials

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Teoria d'operadors --- Anàlisi funcional --- Àlgebres d'operadors --- Equacions d'evolució no lineal --- Operadors diferencials --- Operadors integrals --- Operadors lineals --- Operadors no lineals --- Operadors pseudodiferencials --- Semigrups d'operadors --- Teoria dels operadors --- Operator theory. --- Functional analysis

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This proceedings volume features selected contributions from the conference Positivity X. The field of positivity deals with ordered mathematical structures and their applications. At the biannual series of Positivity conferences, the latest developments in this diverse field are presented. The 2019 edition was no different, with lectures covering a broad spectrum of topics, including vector and Banach lattices and operators on such spaces, abstract stochastic processes in an ordered setting, the theory and applications of positive semi-groups to partial differential equations, Hilbert geometries, positivity in Banach algebras and, in particular, operator algebras, as well as applications to mathematical economics and financial mathematics. The contributions in this book reflect the variety of topics discussed at the conference. They will be of interest to researchers in functional analysis, operator theory, measure and integration theory, operator algebras, and economics. Positivity X was dedicated to the memory of our late colleague and friend, Coenraad Labuschagne. His untimely death in 2018 came as an enormous shock to the Positivity community. He was a prominent figure in the Positivity community and was at the forefront of the recent development of abstract stochastic processes in a vector lattice context.

Teoria d'operadors --- Espais topològics ordenats --- Espais topològics --- Teoria dels operadors --- Anàlisi funcional --- Àlgebres d'operadors --- Equacions d'evolució no lineal --- Operadors diferencials --- Operadors integrals --- Operadors lineals --- Operadors no lineals --- Operadors pseudodiferencials --- Semigrups d'operadors --- Operator theory --- Ordered topological spaces --- Positive operators --- Operators, Positive --- Linear operators --- Spaces, Ordered topological --- Topological spaces

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Teoria d'operadors --- Anàlisi harmònica --- Àlgebres de Banach --- Càlcul --- Àlgebres de mesura --- Harmòniques esfèriques --- Ondetes (Matemàtica) --- Anàlisi de Fourier --- Anàlisi de sèries temporals --- Funcions de Bessel --- Teoria dels operadors --- Anàlisi funcional --- Àlgebres d'operadors --- Equacions d'evolució no lineal --- Operadors diferencials --- Operadors integrals --- Operadors lineals --- Operadors no lineals --- Operadors pseudodiferencials --- Semigrups d'operadors --- Operator theory --- Harmonic analysis

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Teoria d'operadors --- Espais de Hilbert --- Anàlisi funcional --- Àlgebres d'operadors --- Equacions d'evolució no lineal --- Operadors diferencials --- Operadors integrals --- Operadors lineals --- Operadors no lineals --- Operadors pseudodiferencials --- Semigrups d'operadors --- Teoria dels operadors --- Espais de Banach --- Hiperespai --- Teoria espectral (Matemàtica) --- Espai de Hilbert --- Hilbert space. --- Operator theory. --- Functional analysis --- Banach spaces --- Hyperspace --- Inner product spaces