| |

| |

Foreword | |

| |

| |

| |

Elementary Aspects of Potential Theory in Mathematical Physics | |

| |

| |

| |

Introduction | |

| |

| |

| |

The Laplace Differential Operator and the Poisson-Dirichlet Potential Problem | |

| |

| |

| |

The Dirichlet Problem in Connected Planar Regions: A Conformal Transformation Method for Green Functions in String Theory | |

| |

| |

| |

Hilbert Spaces Methods in the Poisson Problem | |

| |

| |

| |

The Abstract Formulation of the Poisson Problem | |

| |

| |

| |

Potential Theory for the Wave Equation in R[superscript 3] - Kirchhoff Potentials (Spherical Means) | |

| |

| |

| |

The Dirichlet Problem for the Diffusion Equation - Seminar Exercises | |

| |

| |

| |

The Potential Theory in Distributional Spaces - The Gelfand-Chilov Method | |

| |

| |

References | |

| |

| |

| |

Light Deflection on de-Sitter Space | |

| |

| |

| |

The Light Deflection | |

| |

| |

| |

The Trajectory Motion Equations | |

| |

| |

| |

On the Topology of the Euclidean Space-Time | |

| |

| |

| |

Scattering Theory in Non-Relativistic One-Body Short-Range Quantum Mechanics: Moller Wave Operators and Asymptotic Completeness | |

| |

| |

| |

The Wave Operators in One-Body Quantum Mechanics | |

| |

| |

| |

Asymptotic Properties of States in the Continuous Spectra of the Enss Hamiltonian | |

| |

| |

| |

The Enss Proof of the Non-Relativistic One-Body Quantum Mechanical Scattering | |

| |

| |

References | |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

On the Hilbert Space Integration Method for the Wave Equation and Some Applications to Wave Physics | |

| |

| |

| |

Introduction | |

| |

| |

| |

The Abstract Spectral Method - The Nondissipative Case | |

| |

| |

| |

The Abstract Spectral Method - The Dissipative Case | |

| |

| |

| |

The Wave Equation "Path-Integral" Propagator | |

| |

| |

| |

On The Existence of Wave-Scattering Operators | |

| |

| |

| |

Exponential Stability in Two-Dimensional Magneto-Elasticity: A Proof on a Dissipative Medium | |

| |

| |

| |

An Abstract Semilinear Klein Gordon Wave Equation - Existence and Uniqueness | |

| |

| |

References | |

| |

| |

| |

Exponential Stability in Two-Dimensional Magneto-Elastic: Another Proof | |

| |

| |

| |

Probability Theory in Terms of Functional Integrals and the Minlos Theorem | |

| |

| |

| |

Nonlinear Diffusion and Wave-Damped Propagation: Weak Solutions and Statistical Turbulence Behavior | |

| |

| |

| |

Introduction | |

| |

| |

| |

The Theorem for Parabolic Nonlinear Diffusion | |

| |

| |

| |

The Hyperbolic Nonlinear Damping | |

| |

| |

| |

A Path-Integral Solution for the Parabolic Nonlinear Diffusion | |

| |

| |

| |

Random Anomalous Diffusion, A Semigroup Approach | |

| |

| |

References | |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

Probability Theory in Terms of Functional Integrals and the Minlos Theorem - An Overview | |

| |

| |

| |

Domains of Bosonic Functional Integrals and Some Applications to the Mathematical Physics of Path-Integrals and String Theory | |

| |

| |

| |

Introduction | |

| |

| |

| |

The Euclidean Schwinger Generating Functional as a Functional Fourier Transform | |

| |

| |

| |

The Support of Functional Measures - The Minlos Theorem | |

| |

| |

| |

Some Rigorous Quantum Field Path-Integral in the Analytical Regularization Scheme | |

| |

| |

| |

Remarks on the Theory of Integration of Functionals on Distributional Spaces and Hilbert-Banach Spaces | |

| |

| |

References | |

| |

| |

| |

| |

| |

| |

On the Support Evaluations of Gaussian Measures | |

| |

| |

| |

Some Calculations of the Q.C.D. Fermion Functional Determinant in Two-Dimensions and (Q.E.D.)[subscript 2] Solubility | |

| |

| |

| |

Functional Determinants Evaluations on the Seeley Approach | |

| |

| |

| |

Basic Integral Representations in Mathematical Analysis of Euclidean Functional Integrals | |

| |

| |

| |

On the Riesz-Markov Theorem | |

| |

| |

| |

The L. Schwartz Representation Theorem on C[superscript infinity] ([Omega]) (Distribution Theory) | |

| |

| |

| |

Equivalence of Gaussian Measures in Hilbert Spaces and Functional Jacobians | |

| |

| |

| |

On the Weak Poisson Problem in Infinite Dimension | |

| |

| |

| |

The Path-Integral Triviality Argument | |

| |

| |

| |

The Loop Space Argument for the Thirring Model Triviality | |

| |

| |

References | |

| |

| |

| |

Path-Integral Solution for a Two-Dimensional Model with Axial-Vector-Current-Pseudoscalar Derivative Interaction | |

| |

| |

| |

Path Integral Bosonization for an Abelian Nonrenormalizable Axial Four-Dimensional Fermion Model | |

| |

| |

| |

Nonlinear Diffusion in R[superscript D] and Hilbert Spaces: A Path-Integral Study | |

| |

| |

| |

Introduction | |

| |

| |

| |

The Nonlinear Diffusion | |

| |

| |

| |

The Linear Diffusion in the Space L[superscript 2]([Omega]) | |

| |

| |

References | |

| |

| |

| |

The Aubin-Lion Theorem | |

| |

| |

| |

The Linear Diffusion Equation | |

| |

| |

| |

On the Ergodic Theorem | |

| |

| |

| |

Introduction | |

| |

| |

| |

On the Detailed Mathematical Proof of the RAGE Theorem | |

| |

| |

| |

On the Boltzmann Ergodic Theorem in Classical Mechanics as a Result of the RAGE Theorem | |

| |

| |

| |

On the Invariant Ergodic Functional Measure for Some Nonlinear Wave Equations | |

| |

| |

| |

An Ergodic Theorem in Banach Spaces and Applications to Stochastic-Langevin Dynamical Systems | |

| |

| |

| |

The Existence and Uniqueness Results for Some Nonlinear Wave Motions in 2D | |

| |

| |

References | |

| |

| |

| |

On Sequences of Random Measureson Functional Spaces | |

| |

| |

| |

On the Existence of Periodic Orbits in a Class of Mechanical Hamiltonian Systems - An Elementary Mathematical Analysis | |

| |

| |

| |

Elementary May be Deep - T. Kato | |

| |

| |

| |

Some Comments on Sampling of Ergodic Process: An Ergodic Theorem and Turbulent Pressure Fluctuations | |

| |

| |

| |

Introduction | |

| |

| |

| |

A Rigorous Mathematical Proof of the Ergodic Theorem for Wide-Sense Stationary Stochastic Process | |

| |

| |

| |

A Sampling Theorem for Ergodic Process | |

| |

| |

| |

A Model for the Turbulent Pressure Fluctuations (Random Vibrations Transmission) | |

| |

| |

References | |

| |

| |

| |

Chapters 1 and 9 - On the Uniform Convergence of Orthogonal Series - Some Comments | |

| |

| |

| |

Fourier Series | |

| |

| |

| |

Regular Sturm-Liouville Problem | |

| |

| |

| |

On the Muntz-Szasz Theorem on Commutative Banach Algebras | |

| |

| |

| |

Introduction | |

| |

| |

| |

Feynman Path-Integral Representations for the Classical Harmonic Oscillator with Stochastic Frequency | |

| |

| |

| |

Introduction | |

| |

| |

| |

The Green Function for External Forcing | |

| |

| |

| |

The Homogeneous Problem | |

| |

| |

| |

An Elementary Comment on the Zeros of the Zeta Function (on the Riemann's Conjecture) | |

| |

| |

| |

Introduction - "Elementary May be Deep" | |

| |

| |

| |

On the Equivalent Conjecture D.1 | |

| |

| |

| |

Some Studies on Functional Integrals Representations for Fluid Motion with Random Conditions | |

| |

| |

| |

Introduction | |

| |

| |

| |

The Functional Integral for Initial Fluid Velocity Random Conditions | |

| |

| |

| |

An Exactly Soluble Path-Integral Model for Stochastic Beltrami Fluxes and its String Properties | |

| |

| |

| |

A Complex Trajectory Path-Integral Representation for the Burger-Beltrami Fluid Flux | |

| |

| |

References | |

| |

| |

| |

A Perturbative Solution of the Burgers Equation Through the Banach Fixed Point Theorem | |

| |

| |

| |

Some Comments on the Support of Functional Measures in Hilbert Space | |

| |

| |

| |

The Atiyah-Singer Index Theorem: A Heat Kernel (PDE's) Proof | |

| |

| |

References | |

| |

| |

| |

Normalized Ricci Fluxes in Closed Riemann Surfaces and the Dirac Operator in the Presence of an Abelian Gauge Connection | |

| |

| |

Index | |