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Author Botelho, Luiz C L
Title Lecture Notes In Applied Differential Equations Of Mathematical Physics
Imprint Singapore : World Scientific Publishing Company, 2008
book jacket
Descript 1 online resource (340 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Note Intro -- Contents -- Foreword -- Chapter 1. Elementary Aspects of Potential Theory in Mathematical Physics -- 1.1. Introduction -- 1.2. The Laplace Differential Operator and the Poisson-Dirichlet Potential Problem -- 1.3. The Dirichlet Problem in Connected Planar Regions: A Conformal Transformation Method for Green Functions in String Theory -- 1.4. Hilbert Spaces Methods in the Poisson Problem -- 1.5. The Abstract Formulation of the Poisson Problem -- 1.6. Potential Theory for the Wave Equation in R3 - Kirchho. Potentials (Spherical Means) -- 1.7. The Dirichlet Problem for the Diffusion Equation - Seminar Exercises -- 1.8. The Potential Theory in Distributional Spaces - The Gelfand-ChilovMethod -- References -- Appendix A. Light Deflection on de-Sitter Space -- A.1.The Light Deflection -- A.2.The Trajectory Motion Equations -- A.3. On the Topology of the Euclidean Space-Time -- Chapter 2. Scattering Theory in Non-Relativistic One-Body Short-Range Quantum Mechanics: M¨oller Wave Operators and Asymptotic Completeness -- 2.1. The Wave Operators in One-Body Quantum Mechanics -- 2.2. Asymptotic Properties of States in the Continuous Spectra of the Enss Hamiltonian -- 2.3. The Enss Proof of the Non-Relativistic One-Body QuantumMechanical Scattering -- References -- Appendix A -- Appendix B -- Appendix C -- Chapter 3. On the Hilbert Space Integration Method for the Wave Equation and Some Applications to Wave Physics -- 3.1. Introduction -- 3.2. The Abstract Spectral Method - The Nondissipative Case -- 3.3. The Abstract Spectral Method - The Dissipative Case -- 3.4. The Wave Equation "Path-Integral" Propagator -- 3.5. On The Existence of Wave-Scattering Operators -- 3.6. Exponential Stability in Two-Dimensional Magneto-Elasticity: A Proof on a Dissipative Medium -- 3.7. An Abstract Semilinear Klein Gordon Wave Equation - Existence and Uniqueness
References -- Appendix A. Exponential Stability in Two-Dimensional Magneto-Elastic: Another Proof -- Appendix B. Probability Theory in Terms of Functional Integrals and theMinlos Theorem -- Chapter 4. Nonlinear Di.usion and Wave-Damped Propagation: Weak Solutions and Statistical Turbulence Behavior. -- 4.1. Introduction -- 4.2. The Theorem for Parabolic Nonlinear Diffusion -- 4.3. The Hyperbolic Nonlinear Damping -- 4.4. A Path-Integral Solution for the Parabolic Nonlinear Diffusion -- 4.5. Random Anomalous Diffuusion, A Semigroup Approach -- References -- Appendix A -- Appendix B -- Appendix C -- Appendix D. Probability Theory in Terms of Functional Integrals and the Minlos Theorem - An Overview -- Chapter 5. Domains of Bosonic Functional Integrals and Some Applications to the Mathematical Physics of Path-Integrals and String Theory -- 5.1. Introduction -- 5.2. The Euclidean Schwinger Generating Functional as a Functional Fourier Transform -- 5.3. The Support of Functional Measures - The Minlos Theorem -- 5.4. Some Rigorous Quantum Field Path-Integral in the Analytical Regularization Scheme -- 5.5. Remarks on the Theory of Integration of Functionals on Distributional Spaces and Hilbert-Banach Spaces -- References -- Appendix A -- Appendix B. On the Support Evaluations of Gaussian Measures -- Appendix C. Some Calculations of the Q.C.D. Fermion Functional Determinant in Two-Dimensions and (Q.E.D.)2 Solubility -- Appendix D. Functional Determinants Evaluations on the Seeley Approach -- Chapter 6. Basic Integral Representations in Mathematical Analysis of Euclidean Functional Integrals. -- 6.1. On the Riesz-Markov Theorem -- 6.2. The L. Schwartz Representation Theorem on C∞() (Distribution Theory) -- 6.3. Equivalence of Gaussian Measures in Hilbert Spaces and Functional Jacobians -- 6.4. On the Weak Poisson Problem in Infinite Dimension
6.5. The Path-Integral Triviality Argument -- 6.6. The Loop Space Argument for the Thirring Model Triviality -- References -- Appendix A. Path-Integral Solution for a Two-Dimensional Model with Axial-Vector-Current-Pseudoscalar Derivative Interaction -- Appendix B. Path Integral Bosonization for an Abelian Nonrenormalizable Axial Four-Dimensional FermionModel -- B.1. Introduction -- B.2. The Model -- B.3. Complement -- Chapter 7. Nonlinear Diffusion in RD and Hilbert Spaces: A Path-Integral Study -- 7.1. Introduction -- 7.2. The Nonlinear Diffusion -- 7.3. The Linear Diffusion in the Space L2(.) -- References -- Appendix A. The Aubin-Lion Theorem -- Appendix B. The Linear Diffusion Equation -- Chapter 8. On the Ergodic Theorem -- 8.1. Introduction -- 8.2. On the Detailed Mathematical Proof of the RAGE Theorem -- 8.3. On the Boltzmann Ergodic Theorem in Classical Mechanics as a Result of the RAGE Theorem -- 8.4. On the Invariant Ergodic Functional Measure for Some NonlinearWave Equations -- 8.5. An Ergodic Theorem in Banach Spaces and Applications to Stochastic-Langevin Dynamical Systems -- 8.6. The Existence and Uniqueness Results for Some Nonlinear Wave Motions in 2D -- References -- Appendix A. On Sequences of Random Measureson Functional Spaces -- Appendix B. On the Existence of Periodic Orbits in a Class of Mechanical Hamiltonian Systems -An Elementary Mathematical Analysis -- B.1. Elementary May be Deep - T. Kato -- Chapter 9. Some Comments on Sampling of Ergodic Process: An Ergodic Theorem and Turbulent Pressure Fluctuations. -- 9.1. Introduction -- 9.2. A Rigorous Mathematical Proof of the Ergodic Theorem for Wide-Sense Stationary Stochastic Process -- 9.3. A Sampling Theorem for Ergodic Process -- 9.4. A Model for the Turbulent Pressure Fluctuations (Random Vibrations Transmission) -- References
Appendix A. Chapters 1 and 9 - On the Uniform Convergence of Orthogonal Series - Some Comments -- A.1. Fourier Series -- A.2. Regular Sturm-Liouville Problem -- Appendix B. On the M¨untz-Szasz Theorem on Commutative Banach Algebras -- B.1. Introduction -- Appendix C. Feynman Path-Integral Representations for the Classical Harmonic Oscillator with Stochastic Frequency -- C.1. Introduction -- C.2. The Green Function for External Forcing -- C.3. The Homogeneous Problem -- Appendix D. An Elementary Comment on the Zeros of the Zeta Function (on the Riemann's Conjecture) -- D.1. Introduction - "Elementary May be Deep" -- D.2.On the Equivalent Conjecture D.1 -- Chapter 10. Some Studies on Functional Integrals Representations for Fluid Motion with Random Conditions -- 10.1. Introduction -- 10.2. The Functional Integral for Initial Fluid Velocity RandomConditions -- 10.3. An Exactly Soluble Path-Integral Model for Stochastic Beltrami Fluxes and its String Properties -- 10.4. A Complex Trajectory Path-Integral Representation for the Burger-Beltrami Fluid Flux -- References -- Appendix A. A Perturbative Solution of the Burgers Equation Through the Banach Fixed Point Theorem -- Appendix B. Some Comments on the Support of Functional Measures in Hilbert Space -- Chapter 11. The Atiyah-Singer Index Theorem: A Heat Kernel (PDE's) Proof -- References -- Appendix A. Normalized Ricci Fluxes in Closed Riemann Surfaces and the Dirac Operator in the Presence of an Abelian Gauge Connection -- Index
Key Features:Includes a unique treatment of Euclidean path integrals through the unifying concept of the Minlos theorem in support of cylindrical measuresPresents solutions to stochastic and Hilbert valued differential equations by means of path integrals in mathematical detail
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Botelho, Luiz C L Lecture Notes In Applied Differential Equations Of Mathematical Physics Singapore : World Scientific Publishing Company,c2008 9789812814579
Subject Differential equations.;Functional analysis.;Mathematical physics
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