Generalized Functions, Convergence Structures, and Their Applications

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 withdiscontinuous 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.