LEADER 05372nam 2200649Ia 450 001 9910455545103321 005 20200520144314.0 010 $a981-281-458-2 035 $a(CKB)1000000000766619 035 $a(EBL)1193652 035 $a(SSID)ssj0000455388 035 $a(PQKBManifestationID)11346152 035 $a(PQKBTitleCode)TC0000455388 035 $a(PQKBWorkID)10400012 035 $a(PQKB)11325959 035 $a(MiAaPQ)EBC1193652 035 $a(WSP)00006856 035 $a(Au-PeEL)EBL1193652 035 $a(CaPaEBR)ebr10688008 035 $a(CaONFJC)MIL498379 035 $a(OCoLC)820944533 035 $a(EXLCZ)991000000000766619 100 $a20090204d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLecture notes in applied differential equations of mathematical physics$b[electronic resource] /$fLuiz C.L. Botelho 210 $aHackensack, NJ $cWorld Scientific$dc2008 215 $a1 online resource (340 p.) 300 $aIncludes index. 311 $a981-281-457-4 320 $aIncludes bibliographical references and index. 327 $aForeword; Contents; 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 327 $a1.8. The Potential Theory in Distributional Spaces - The Gelfand-ChilovMethodReferences; 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 327 $a2.3. The Enss Proof of the Non-Relativistic One-Body QuantumMechanical ScatteringReferences; 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 327 $a3.7. An Abstract Semilinear Klein Gordon Wave Equation - Existence and UniquenessReferences; 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 327 $a4.5. Random Anomalous Diffuusion, A Semigroup ApproachReferences; 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 327 $a5.5. Remarks on the Theory of Integration of Functionals on Distributional Spaces and Hilbert-Banach Spaces 330 $aFunctional analysis is a well-established powerful method in mathematical physics, especially those mathematical methods used in modern non-perturbative quantum field theory and statistical turbulence. This book presents a unique, modern treatment of solutions to fractional random differential equations in mathematical physics. It follows an analytic approach in applied functional analysis for functional integration in quantum physics and stochastic Langevin-turbulent partial differential equations.An errata II to the book is available. Click here to download the pdf. 606 $aDifferential equations 606 $aFunctional analysis 606 $aMathematical physics 608 $aElectronic books. 615 0$aDifferential equations. 615 0$aFunctional analysis. 615 0$aMathematical physics. 676 $a530.15535 700 $aBotelho$b Luiz C. 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