Generalized Functions, Convergence Structures, and Their Applications

Front Matter....Pages i-xi
Front Matter....Pages 1-1
Nonharmonic Solutions of the Laplace Equation....Pages 3-11
Generalized Functions; Multiplication of Distributions; Applications to Elasticity, Elastoplasticity, Fluid Dynamics and Acoustics....Pages 13-27
Monads and Convergence....Pages 29-46
Simple Applications of Generalized Functions in Theoretical Physics: The Case of Many–Body Perturbation Expansions....Pages 47-55
Laplace Transforms of Hyperfunctions: Another Foundation of the Heaviside Operational Calculus....Pages 57-70
S-Asymptotic of Distributions....Pages 71-82
The Wiener-Hopf Equation in the Nevanlinna and Smirnov Algebras and Ultra-Distributions....Pages 83-96
Front Matter....Pages 97-97
On Nonlinear Systems of Ordinary Differential Equations....Pages 99-111
A New Construction of Continuous Endomorphisms of the Operator Field....Pages 113-119
Some Comments on the Burzyk-Paley-Wiener Theorem for Regular Operators....Pages 121-124
Two Theorems on the Differentiation of Regular Convolution Quotients....Pages 125-129
Values on the Topological Boundary of Tubes....Pages 131-138
Abelian Theorem for the Distributional Stieltjes Transformation....Pages 139-146
Some Results on the Neutrix Convolution Product of Distributions....Pages 147-155
On Generalized Transcedental Functions and Distributional Transforms....Pages 157-170
An Algebraic Approach to Distribution Theories....Pages 171-177
Products of Wiener Functionals on an Abstract Wiener Space....Pages 179-185
Convolution in K’ {M p }-Spaces....Pages 187-196
The Problem of the Jump and the Sokhotski Formulas in the Space of Generalized Functions on a Segment of the Real Axis....Pages 197-203
A Generalized Fractional Calculus and Integral Transforms....Pages 205-217
Front Matter....Pages 97-97
On the Generalized Meijer Transformation....Pages 219-225
The Construction of Regular Spaces and Hyperspaces with Respect to a Particular Operator....Pages 227-233
Operational Calculus with Derivative Ŝ = S 2 ....Pages 235-243
Solvability of Nonlinear Operator Equations with Applications to Hyperbolic Equations....Pages 245-250
Some Important Results of Distribution Theory....Pages 251-255
Hyperbolic Systems with Discontinuous Coefficients: Examples....Pages 257-266
Estimations for the Solutions of Operator Linear Differential Equations....Pages 267-277
Invariance of the Cauchy Problem for Distribution Differential Equations....Pages 279-284
On the Space $$\upsilon _{{\text{L}}^{\text{q}} }^{'\,^{\left( {{\text{M}}_{\text{p}} } \right)} } $$ , q ∈ [1,∞]....Pages 285-295
Peetre’s Theorem and Generalized Functions....Pages 297-304
Infinite Dimensional Fock Spaces and an Associated Generalized Laplacian Operator....Pages 305-316
The n-Dimensional Stieltjes Transformation....Pages 317-325
Colombeau’s Generalized Functions and Non-Standard Analysis....Pages 327-339
One Product of Distributions....Pages 341-348
Abel Summability for a Distribution Sampling Theorem....Pages 349-357
On the Value of a Distribution at a Point....Pages 359-364
Front Matter....Pages 365-365
On Interchange of Limits....Pages 367-374
Countability, Completeness and the Closed Graph Theorem....Pages 375-381
Inductive Limits of Riesz Spaces....Pages 383-392
Convergence Completion of Partially Ordered Groups....Pages 393-398
Front Matter....Pages 365-365
Some Results from Nonlinear Analysis in Limit Vector Spaces....Pages 399-407
Completions of Cauchy Vector Spaces....Pages 409-414
Regular Inductive Limits....Pages 415-418
Weak Convergence in a K-Space....Pages 419-423
The Banach-Steinhaus Theorem for Ordered Spaces....Pages 425-432
Front Matter....Pages 433-433
Open Problems....Pages 435-441
Back Matter....Pages 443-452