TY - GEN

AU - Stanković, Bogoljub

AU - Pap, Endre

AU - Pilipović, Stevan

AU - Vladimirov, Vasilij S.

TI - Generalized Functions, Convergence Structures, and Their Applications

PB - Springer US

SN - 9781461310556

KW - Computer science

KW - Mathematical analysis.

PY - 1988

N2 - Section I. Plenary LecturesNonharmonic 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.

CY - Boston, MA

UR - http://slubdd.de/katalog?TN_libero_mab2

ER -