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Applied Differential Equations of Mathematical Physics
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Applied Differential Equations of Mathematical Physics

Botelho, Luiz C. L.
ISBN-10: 9812814574
ISBN-13: 9789812814579

In our Marketplace:
1 new from $103.01
"Functional 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."--BOOK JACKET.
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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

List price: $91.00
Edition: 2008
Publisher: World Scientific Publishing Company, Incorporated
Binding: Trade Cloth
Pages: N/A
Size: 6.25" wide x 9.25" long x 1.00" tall
Weight: 1.39 lbs.
Language: English

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