These Proceedings form a record of the lectures presented at the interna­ tional Conference on Functional Analysis and Approximation held at the Ober­ wolfach Mathematical Research Institute, August 9-16, 1980. They include 33 of the 38 invited conference papers, as well as three papers subsequently submitted in writing. Further, there is a report devoted to new and unsolved problems, based on two special sessions of the conference. The present volume is the sixth Oberwolfach Conference in Birkhauser's ISNM series to be edited at Aachen *. It is once again devoted to more significant results obtained in the wide areas of approximation theory, harmonic analysis, functional analysis, and operator theory during the past three years. Many of the papers solicited not only outline fundamental advances in their fields but also focus on interconnections between the various research areas. The papers in the present volume have been grouped into nine chapters. Chapter I, on operator theory, deals with maps on positive semidefinite opera­ tors, spectral bounds of semigroup operators, evolution equations of diffusion type, the spectral theory of propagators, and generalized inverses. Chapter II, on functional analysis, contains papers on modular approximation, interpolation spaces, and unconditional bases.

Inhalt

Zur Tagung.- List of participants.- Program of the Sessions.- Jacob Lionel Bakst Cooper - in memoriam.- A testimony from a friend.- I Operator Theory.- Fixed points of certain maps on positive semidefinite operators.- A remark on the spectral bound of the generator of semigroups of positive operators with applications to stability theory.- Local operators, regular sets, and evolution equations of diffusion type.- An outline of the spectral theory of propagators.- On generalized inverses and operator ranges.- II Functional Analysis.- Modular approximation by a filtered family of linear operators.- Interpolation between H1 and L?.- The Franklin orthogonal system as unconditional basis in ReH1 and VMO.- III Abstract Harmonic Analysis.- Bessel potential spaces and generalized Lipschitz spaces on local fields.- On the minimum norm property of the Fourier projection in L1-spaces.- Banach spaces of distributions of Wiener's type and interpolation.- Approximation theory on the compact solenoid.- IV Fourier Analysis and Integral Transforms.- J. Szabados: Bernstein and Markov type estimates for the derivative of a polynomial with real zeros.- Projections with norms smaller than those of the ultraspherical and Laguerre partial sums.- The regular convergence of multiple series.- Norm inequalities relating the Hilbert transform to the Hardy-Littlewood maximal function.- Best approximation on the unit sphere in Rk.- V Best Approximation.- Ein Problem über die beste Approximation in Hilberträumen.- Über Existenz- und Eindeutigkeitsmengen bei der besten Ko-Approximation.- Inverse approximation theorems of Lebedev and Tamrazov.- Best multipoint local approximation.- VI Approximation by Linear Operators.- On the Lebesgue function of interpolation.- A uniform boundedness principle with rates and an application to linear processes.- Slow approximation with convolution operators.- A remark on asymptotically optimal approximation by Faber series.- VII Strong and Miintz Approximation.- Strong approximation and generalized Lipschitz classes.- Strong approximation and the behaviour of Fourier series.- On the rate of approximation by Müntz polynomials satisfying constraints.- VIII Number Theory and Probability.- The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces.- On the approximation of indicator functions by smooth functions in Banach spaces.- On the o-closeness of the distribution of two weighted sums of Banach space valued martingales with applications.- IX Splines and Numerical Integration.- Approximation und Transformationsmethoden III.- Uniqueness of optimal piecewise polynomial L1 approximations for generalized convex functions.- The dominated integral of functions of two variables.- Bernstein-Polynome, 1912-1955.- New and unsolved problems.- Errata.- Alphabetical list of papers.- Mathematics subject classification numbers.- Key words and phrases.