05066nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001600172072001700188072002300205072001600228100008400244245016200328250001800490264006900508300003600577336002600613337002600639338003600665347002400701490005300725505200000778520124602778650002504024650004204049650003604091650002804127650002504155650005404180650002804234710003404262773002604296776003604322776003604358830006004394856004604454912001404500912001504514912001404529999001704543978-3-031-66612-4DE-He21320251030113051.0cr nn 008mamaa240918s2024    sz |    s    |||| 0|eng d  a97830316661249978-3-031-66612-47 a10.1007/978-3-031-66612-42doi 4aQA319-329.9 7aPBKF2bicssc 7aMAT0370002bisacsh 7aPBKF2thema1 aTaira, Kazuaki.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98357210aFunctional Analytic Methods for Heat Green Operatorsh[electronic resource] :bHeat Kernel Asymptotics via the Weyl-Hörmander Calculus /cby Kazuaki Taira.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXVIII, 644 p.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aLecture Notes in Mathematics,x1617-9692 ;v23540 a- Introduction and Main Results -- Part I Functional Analytic Approach to Heat Operators -- Preliminaries from Manifold Theory -- Finite Double-Norm and Trace-Class Operators on a Hilbert Space -- Hilbert–Schmidt and Trace-Class Operators on a Manifold -- Analytic Semigroups via Dunford Integrals -- Part II Pseudo-Differential Operators and Elliptic Boundary Value Problems -- Lp Theory of Pseudo-Differential Operators -- Elliptic Boundary Value Problems on a Manifold -- Lp Theory of Elliptic Boundary Value Problems -- Boutet de Monvel Calculus -- Pseudo-Differential Operator Approach to Agmon’s Method -- Part III Analytic Semigroup Approach to Heat Operators -- Generation Theorem for Analytic Semigroups via Agmon’s Method -- Hypoelliptic Robin Problems via Boutet de Monvel Calculus -- Distribution Kernel of Analytic Semigroups in the Hypoelliptic Case -- Part IV The Fundamental Solution for the Cauchy Problem -- The Cauchy Problem for the Heat Operator on Rn -- Fundamental Solution Operator for the Cauchy Problem on a Manifold -- Part V Symbolic Calculus for Dirichlet, Neumann and Regular Robin Problems -- Symbolic Calculus near the Boundary -- Analytic Version of Weyl Bases for the Heat Kernel on the Half Axis -- Symbolic Calculus for Boundary Value Problems on a Manifold -- Part VI Transport Equations and Trace Formulas on the Half Space -- Transport Equations via the Weyl–Hörmander Calculus -- Several Trace Formulas for Auxiliary Operators on the Half Space -- Part VII Heat Kernel Asymptotics for Dirichlet, Neumann and Regular Robin Problems -- Heat Kernel Asymptotics for the Dirichlet Problem -- Heat Kernel Asymptotics for the Neumann Problem -- Heat Kernel Asymptotics for the Regular Robin Problem -- Heat Kernel Asymptotics for the Generalized Regular Robin Problem -- Part VIII Heat Kernel Asymptotics for the Hypoelliptic Robin Problem -- Heat Kernel Asymptotics for the Hypoelliptic Robin Problem -- Examples in the Plane R2 -- Concluding Remarks.  aThis monograph guides the reader to the mathematical crossroads of heat equations and differential geometry via functional analysis. Following the recent trend towards constructive methods in the theory of partial differential equations, it makes extensive use of the ideas and techniques from the Weyl–Hörmander calculus of pseudo-differential operators to study heat Green operators through concrete calculations for the Dirichlet, Neumann, regular Robin and hypoelliptic Robin boundary conditions. Further, it provides detailed coverage of important examples and applications in elliptic and parabolic problems, illustrated with many figures and tables. A unified mathematical treatment for solving initial boundary value problems for the heat equation under general Robin boundary conditions is desirable, and leads to an extensive study of various aspects of elliptic and parabolic partial differential equations. The principal ideas are explicitly presented so that a broad spectrum of readers can easily understand the problem and the main results. The book will be of interest to readers looking for a functional analytic introduction to the meeting point of partial differential equations, differential geometry and probability. 0aFunctional analysis. 0aGlobal analysis (Mathematics).969682 0aManifolds (Mathematics).969683 0aDifferential equations.14aFunctional Analysis.24aGlobal Analysis and Analysis on Manifolds.96968524aDifferential Equations.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303166611708iPrinted edition:z9783031666131 0aLecture Notes in Mathematics,x1617-9692 ;v235497543440uhttps://doi.org/10.1007/978-3-031-66612-4  aZDB-2-SMA  aZDB-2-SXMS  aZDB-2-LNM  c63504d63504