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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-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 |
2.3. 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 |
3.7. 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 |
4.5. 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 |
5.5. Remarks on the Theory of Integration of Functionals on Distributional Spaces and Hilbert-Banach Spaces |