Analysis of Divergence: Control and Management of Divergent Processes(Applied and Numerical Harmonic Analysis)

The 7th International Workshop in Analysis and its Applications (IWAA) was held at the University of Maine, June 1-6, 1997 and featured approxi­ mately 60 mathematicians. The principal theme of the workshop shares the title of this volume and the latter is a direct outgrowth of the workshop. IWAA was founded in 1984 by Professor Caslav V. Stanojevic. The first meeting was held in the resort complex Kupuri, Yugoslavia, June 1-10, 1986, with two pilot meetings preceding. The Organization Committee to­ gether with the Advisory Committee (R. P. Boas, R. R. Goldberg, J. P. Kahne) set forward the format and content of future meetings. A certain number of papers were presented that later appeared individually in such journals as the Proceedings of the AMS, Bulletin of the AMS, Mathematis­ chen Annalen, and the Journal of Mathematical Analysis and its Applica­ tions. The second meeting took place June 1-10, 1987, at the same location. At the plenary session of this meeting it was decided that future meetings should have a principal theme. The theme for the third meeting (June 1- 10, 1989, Kupuri) was Karamata's Regular Variation. The principal theme for the fourth meeting (June 1-10, 1990, Kupuri) was Inner Product and Convexity Structures in Analysis, Mathematical Physics, and Economics. The fifth meeting was to have had the theme, Analysis and Foundations, organized in cooperation with Professor A. Blass (June 1-10, 1991, Kupuri).

Table of Contents:
Overview.- I Convergence and Summability.- 1 Tauberian theorems for generalized Abelian summability methods.- 2 Series summability of complete biorthogonal sequences.- 3 Growth of Cesàro means of double Vilenkin-Fourier series of unbounded type.- 4 A substitute for summability in wavelet expansions.- 5 Expansions in series of Legendre functions.- 6 Endpoint convergence of Legendre series.- 7 Inversion of the horocycle transform on real hyperbolic spaces via a wavelet-like transform.- 8 Fourier-Bessel expansions with general boundary conditions.- II Singular Integrals and Multipliers.- 9 Convolution Calderón-Zygmund singular integral operators with rough kernels.- 10 Haar multipliers, paraproducts, and weighted inequalities.- 11 Multipliers and square functions for Hp spaces over Vilenkin groups.- 12 Spectra of pseudo-differential operators in the Hörmander class.- 13 Scaling properties of infinitely flat curves and surfaces.- 14 Some Lp(L?)- and L2(L2)- estimates for oscillatory Fourier transforms.- 15 Optimal spaces for the S’-convolution with the Marcel Riesz kernels and the N-dimensional Hilbert kernel.- III Integral Operators and Functional Analysis.- 16 Asymptotic expansions and linear wavelet packets on certain hypergroups.- 17 Hardy-type inequalities for a new class of integral operators.- 18 Regularly bounded functions and Hardy’s inequality.- 19 Extremal problems in generalized Sobolev classes.- 20 On angularly perturbed Laplace equations in the unit ball and their distributional boundary values.- 21 Nonresonant semilinear equations and applications to boundary value problems.- 22 A topological and functional analytic approach to statistical convergence.- IV Asymptotics and Applications.- 23 Optimal control of divergent control systems.- 24 Surfacesminimizing integrals of divergent integrands.- 25 Sparse exponential sums with low sidelobes.- 26 Spline type summability for multivariate sampling.- 27 B-Splines and orthonormal sets in Paley-Wiener space.- 28 Norms of powers and a central limit theorem.- 29 Quasiasymptotics at zero and nonlinear problems in a framework of Colombeau generalized functions.