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 Call number: SPRINGER-1988-9781461310556:ONLINE Show nearby items on shelf Title: Generalized Functions, Convergence Structures, and Their Applications Author(s): Date: 1988 Size: 1 online resource (464 p.) Note: 10.1007/978-1-4613-1055-6 Contents: Section I. Plenary Lectures -- Nonharmonic solutions of the Laplace equation -- Generalized functions multiplication of distributions applications to elasticity, elastoplasticity, fluid dynamics and acoustics -- Monads and convergence -- Simple applications of generalized functions in theoretical physics: the case of many-body perturbation expansions -- Laplace transforms of hyperfunctions: another foundation of the Heaviside operational calculus -- S-asymptotic of distributions -- The Wiener-Hopf equation in the Nevanlinna and Smirnov algebras and ultradistributions -- Section II. Generalized Functions -- On nonlinear systems of ordinary differential equations -- A new construction of continuous endomorphisms of the operator field -- Some comments on the Burzyk-Paley-Wiener theorem for regular operators -- Two theorems on the differentiation of regular convolution quotients -- Values on the topological boundary of tubes -- Abelian theorem for the distributional Stieltjes transformation -- Some results on the neutrix convolution product of distributions -- On generalized transcedental functions and distributional transforms -- An algebraic approach to distribution theories -- Products of Wiener functionals on an abstract Wiener space -- Convolution in K’{Mp}-spaces -- The problem of the jump and the Sokhotski formulas in the space of generalized functions on a segment of the real axis -- A generalized fractional calculus and integral transforms -- On the generalized Meijer transformation -- The construction of regular spaces and hyperspaces with respect to a particular operator -- Operational calculus with derivative ? = S2 -- Solvability of nonlinear operator equations with applications to hyperbolic equations -- Some important results of distribution theory -- Hyperbolic systems with discontinuous coefficients: examples -- Estimations for the solutions of operator linear differential equations -- Invariance of the Cauchy problem for distribution differential equations -- On the space $$\upsilon _{{\text{L}}^{\text{q}} }^{\prime\,^{\left( {{\text{M}}_{\text{p}} } \right)} }$$ , q ? [1, ?] -- Peetre’s theorem and generalized functions -- Infinite dimensional Fock spaces and an associated generalized Laplacian operator -- The n–dimensional Stieltjes transformation -- Colombeau’s generalized functions and non-standard analysis -- One product of distributions -- Abel summability for a distribution sampling theorem -- On the value of a distribution at a point -- Section III. Convergence Structures -- On interchange of limits -- Countability, completeness and the closed graph theorem -- Inductive limits of Riesz spaces -- Convergence completion of partially ordered groups -- Some results from nonlinear analysis in limit vector spaces -- Completions of Cauchy vector spaces -- Regular inductive limits -- Weak convergence in a K-space -- The Banach-Steinhaus theorem for ordered spaces -- Section IV. Open Problems -- Open problems -- Participants ISBN: 9781461310556 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Keywords: Mathematics , Computer science , Mathematical analysis , Analysis (Mathematics) , Mathematics , Analysis , Computer Science, general Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE