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| Foreword | |
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| Elementary Aspects of Potential Theory in Mathematical Physics | |
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| Introduction | |
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| The Laplace Differential Operator and the Poisson-Dirichlet Potential Problem | |
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| The Dirichlet Problem in Connected Planar Regions: A Conformal Transformation Method for Green Functions in String Theory | |
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| Hilbert Spaces Methods in the Poisson Problem | |
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| The Abstract Formulation of the Poisson Problem | |
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| Potential Theory for the Wave Equation in R[superscript 3] - Kirchhoff Potentials (Spherical Means) | |
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| The Dirichlet Problem for the Diffusion Equation - Seminar Exercises | |
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| The Potential Theory in Distributional Spaces - The Gelfand-Chilov Method | |
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| References | |
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| Light Deflection on de-Sitter Space | |
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| The Light Deflection | |
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| The Trajectory Motion Equations | |
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| On the Topology of the Euclidean Space-Time | |
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| Scattering Theory in Non-Relativistic One-Body Short-Range Quantum Mechanics: Moller Wave Operators and Asymptotic Completeness | |
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| The Wave Operators in One-Body Quantum Mechanics | |
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| Asymptotic Properties of States in the Continuous Spectra of the Enss Hamiltonian | |
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| The Enss Proof of the Non-Relativistic One-Body Quantum Mechanical Scattering | |
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| References | |
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| On the Hilbert Space Integration Method for the Wave Equation and Some Applications to Wave Physics | |
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| Introduction | |
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| The Abstract Spectral Method - The Nondissipative Case | |
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| The Abstract Spectral Method - The Dissipative Case | |
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| The Wave Equation "Path-Integral" Propagator | |
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| On The Existence of Wave-Scattering Operators | |
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| Exponential Stability in Two-Dimensional Magneto-Elasticity: A Proof on a Dissipative Medium | |
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| An Abstract Semilinear Klein Gordon Wave Equation - Existence and Uniqueness | |
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| References | |
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| Exponential Stability in Two-Dimensional Magneto-Elastic: Another Proof | |
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| Probability Theory in Terms of Functional Integrals and the Minlos Theorem | |
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| Nonlinear Diffusion and Wave-Damped Propagation: Weak Solutions and Statistical Turbulence Behavior | |
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| Introduction | |
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| The Theorem for Parabolic Nonlinear Diffusion | |
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| The Hyperbolic Nonlinear Damping | |
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| A Path-Integral Solution for the Parabolic Nonlinear Diffusion | |
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| Random Anomalous Diffusion, A Semigroup Approach | |
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| References | |
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| Probability Theory in Terms of Functional Integrals and the Minlos Theorem - An Overview | |
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| Domains of Bosonic Functional Integrals and Some Applications to the Mathematical Physics of Path-Integrals and String Theory | |
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| Introduction | |
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| The Euclidean Schwinger Generating Functional as a Functional Fourier Transform | |
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| The Support of Functional Measures - The Minlos Theorem | |
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| Some Rigorous Quantum Field Path-Integral in the Analytical Regularization Scheme | |
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| Remarks on the Theory of Integration of Functionals on Distributional Spaces and Hilbert-Banach Spaces | |
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| References | |
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| On the Support Evaluations of Gaussian Measures | |
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| Some Calculations of the Q.C.D. Fermion Functional Determinant in Two-Dimensions and (Q.E.D.)[subscript 2] Solubility | |
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| Functional Determinants Evaluations on the Seeley Approach | |
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| Basic Integral Representations in Mathematical Analysis of Euclidean Functional Integrals | |
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| On the Riesz-Markov Theorem | |
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| The L. Schwartz Representation Theorem on C[superscript infinity] ([Omega]) (Distribution Theory) | |
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| Equivalence of Gaussian Measures in Hilbert Spaces and Functional Jacobians | |
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| On the Weak Poisson Problem in Infinite Dimension | |
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| The Path-Integral Triviality Argument | |
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| The Loop Space Argument for the Thirring Model Triviality | |
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| References | |
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| Path-Integral Solution for a Two-Dimensional Model with Axial-Vector-Current-Pseudoscalar Derivative Interaction | |
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| Path Integral Bosonization for an Abelian Nonrenormalizable Axial Four-Dimensional Fermion Model | |
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| Nonlinear Diffusion in R[superscript D] and Hilbert Spaces: A Path-Integral Study | |
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| Introduction | |
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| The Nonlinear Diffusion | |
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| The Linear Diffusion in the Space L[superscript 2]([Omega]) | |
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| References | |
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| The Aubin-Lion Theorem | |
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| The Linear Diffusion Equation | |
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| On the Ergodic Theorem | |
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| Introduction | |
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| On the Detailed Mathematical Proof of the RAGE Theorem | |
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| On the Boltzmann Ergodic Theorem in Classical Mechanics as a Result of the RAGE Theorem | |
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| On the Invariant Ergodic Functional Measure for Some Nonlinear Wave Equations | |
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| An Ergodic Theorem in Banach Spaces and Applications to Stochastic-Langevin Dynamical Systems | |
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| The Existence and Uniqueness Results for Some Nonlinear Wave Motions in 2D | |
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| References | |
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| On Sequences of Random Measureson Functional Spaces | |
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| On the Existence of Periodic Orbits in a Class of Mechanical Hamiltonian Systems - An Elementary Mathematical Analysis | |
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| Elementary May be Deep - T. Kato | |
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| Some Comments on Sampling of Ergodic Process: An Ergodic Theorem and Turbulent Pressure Fluctuations | |
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| Introduction | |
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| A Rigorous Mathematical Proof of the Ergodic Theorem for Wide-Sense Stationary Stochastic Process | |
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| A Sampling Theorem for Ergodic Process | |
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| A Model for the Turbulent Pressure Fluctuations (Random Vibrations Transmission) | |
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| References | |
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| Chapters 1 and 9 - On the Uniform Convergence of Orthogonal Series - Some Comments | |
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| Fourier Series | |
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| Regular Sturm-Liouville Problem | |
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| On the Muntz-Szasz Theorem on Commutative Banach Algebras | |
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| Introduction | |
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| Feynman Path-Integral Representations for the Classical Harmonic Oscillator with Stochastic Frequency | |
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| Introduction | |
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| The Green Function for External Forcing | |
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| The Homogeneous Problem | |
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| An Elementary Comment on the Zeros of the Zeta Function (on the Riemann's Conjecture) | |
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| Introduction - "Elementary May be Deep" | |
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| On the Equivalent Conjecture D.1 | |
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| Some Studies on Functional Integrals Representations for Fluid Motion with Random Conditions | |
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| Introduction | |
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| The Functional Integral for Initial Fluid Velocity Random Conditions | |
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| An Exactly Soluble Path-Integral Model for Stochastic Beltrami Fluxes and its String Properties | |
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| A Complex Trajectory Path-Integral Representation for the Burger-Beltrami Fluid Flux | |
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| References | |
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| A Perturbative Solution of the Burgers Equation Through the Banach Fixed Point Theorem | |
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| Some Comments on the Support of Functional Measures in Hilbert Space | |
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| The Atiyah-Singer Index Theorem: A Heat Kernel (PDE's) Proof | |
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| References | |
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| Normalized Ricci Fluxes in Closed Riemann Surfaces and the Dirac Operator in the Presence of an Abelian Gauge Connection | |
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| Index | |