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In this work we derive upper Gaussian bounds for the heat kernel on locally symmetric spaces of non-compact type. Furthermore, we determine explicitly the Lp-spectrum of locally symmetric spaces M whose universal covering is a rank one symmetric space of non-compact type if either the fundamental group of M is small (in a certain sense) or if the fundamental group is arithmetic and M is non-compact.

Laplace-Beltrami-Operator --- Wärmeleitungskern --- Lokal symmetrischer Raum --- Spektrum

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Mathematics --- Computer science --- Computer science. --- Mathematics. --- Math --- Informatics --- Operator theory --- Control theory --- Algebraic structures --- Geometry --- Applied mathematics --- Computer science --- Science --- operator theory --- control theory --- algebraic structures --- geometry --- applied mathematics --- computer science

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This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact

Fractional derivative --- fractional Newell-Whitehead-Segel equation --- fractional advection-dispersion equation --- fractional Laguerre differential equation --- Mittag-Leffler function --- sinc-fractional derivative --- tempered fractionaldifferential equation --- Lévy flight --- Marichev-Saigo-Maeda fractional operator --- scale-dependent fractional operator

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Outil de base dans les domaines des équations aux dérivées partielles et de l'analyse sur les variétés, les opérateurs pseudo- différentiels permettent de porter un regard neuf sur la méthode de perturbation de Nash et Moser. Analyse microlocale, théorie de Littlewood-Paley, inégalités d'énergie pour les équations hyperboliques et théorèmes de fonctions implicites sont abordés.

Pseudodifferential operators. --- Implicit functions. --- Functions, Implicit --- Functions of several real variables --- Operators, Pseudodifferential --- Pseudo-differential operators --- Operator theory

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This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schrödinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering.

Operator theory. --- Differential equations. --- Partial differential equations. --- System theory. --- Operator Theory. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Systems Theory, Control. --- Systems, Theory of --- Systems science --- Science --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Functional analysis --- Philosophy --- Mathematics --- Operator theory --- System theory --- Differential equations, Partial.