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TitleLinear Operators and Approximation / Lineare Operatoren und Approximation [electronic resource] : Proceedings of the Conference held at the Oberwolfach Mathematical Research Institute, Black Forest, August 14-22, 1971 / Abhandlungen zur Tagung im Mathematischen Forschungsinstitut Oberwolfach, Schwarzwald, vom 14. bis 22. August 1971 / edited by P. L. Butzer, J.-P. Kahane, B. Szรถkefalvi-Nagy
ImprintBasel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1972
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Descript 506 p. online resource


These proceedings contain the lectures presented at the Conference on Linear Operators and Approximation held at the Oberwolfach Mathematical Research Inยญ stitute, August 14-22, 1971. There were thirty-eight such lectures while four addiยญ tional papers, subsequently submitted in writing, are also included in this volume. Two of the three lectures presented by Russian mathematicians are rendered in English, the third in Russian. Furthermore, there is areport on new and unsolved problems based upon special problem sessions, with later communications from the participants. In fact, two of the papers inc1uded are devoted to solutions of some of the problems posed. The papers have been classified according to subject matter into five chapters, but it needs little emphasis that such thematic groupings are necessarily somewhat arbitrary. Thus Chapter I on Operator Theory is concerned with linear and nonยญ linear semi-groups, structure of single operators, unitary operators, spectral and ergodic theory. Chapter Il on Topics in Functional Analysis inc1udes papers on Riesz spaces, boundedness theorems, generalized limits, and distributions. Chapter III, entitled "Approximation in Abstract Spaces", ranges from characterizations of c1asses of functions in approximation theory to approximation-theoretical topics connected with extensions to Banach (or more general) spaces. Chapter IV contains papers on harmonic analysis in connection with approximation and, finally, Chapter V is devoted to approximation by splines, algebraic polynomials, rational functions, and to Pade approximation. A large part of the general editorial work connected with these proceedings was competently handled by Miss F. Feber, while G


I. Operator Theory -- Generalizations of Landauโ{128}{153}s inequality -- Semi-groups of nonlinear transformations -- Singular perturbations of semi-group generators -- Cyclic vectors and commutants -- Some applications of operator valued analytic functions of two complex variables -- Weylโ{128}{153}s theorems -- Some approximation problems in the theory of stationary processes -- Ein Operatorenkalkรผl fรผr das approximationstheoretische Verhalten des Ergodensatzes im Mittel. -- A note on the Landauโ{128}{148}Kallmannโ{128}{148}Rotaโ{128}{148}Hille inequality -- II. Topics in Functional Analysis -- Representation theorems for Riesz spaces -- Boundedness from measure theory -- Exchange of infinite summation with limits in Banach spaces -- Finite parts of distributions -- Courants et courants cylindriques sur des variรฉtรฉs de dimension infinie -- Subdefinite functions -- Eine Bemerkung zum Banachschen Fixpunktsatz. -- On a certain converse of Hรถlderโ{128}{153}s inequality -- III. Approximation in Abstract Spaces -- On some geometric properties of the unit sphere -- Diskrete Konvergenz linearer Operatoren III -- On set-valued metric projections -- On the comparison of approximation processes in Hubert spaces -- Sรคtze vom Jackson-Typ auf Darstellungsrรคumen kompakter, zusammenhรคngender Liegruppen -- Approximation dโ{128}{153}espaces de fonctions C? et interpolation -- Nonlinear transformations with the conservation of differential properties of functions -- Positive and monotone approximation -- Sรคtze vom Bohmannโ{128}{148}Korowkin-Typ fรผr Banachsche Funktionenrรคume -- IV. Harmonic Analysis and Approximation -- Projection mรฉtrique de L1 (T) sur des sous-espaces fermรฉs invariants par translation -- Bases dans H1 et bases de sous-espaces de dimension finie dans A -- Logarithmic and exponential variants of Bernsteinโ{128}{153}s inequality and generalized derivatives -- Fourier multipliers whose multiplier norm is an attained value -- Nikolskรผ constants for positive singular integrals of perturbed Fejรฉr-type -- A pointwise โ{128}{156}oโ{128}{157} saturation theorem for positive convolution operators -- Convolution operators for Fourierโ{128}{148}Jacobi expansions -- V. Spline- and Algebraic Approximation -- Cardinal interpolation and spline functions IV. The exponential Euler splines -- ?????????? ???????? ? ?????? ??????????? (Anwendungen von Splines in der Approximationstheorie) 419 -- The fundamental theorem of algebra for monosplines with multiplicities -- A contribution to the problem of weighted polynomial approximation -- Zur Konvergenz der Stufenpolynome รผber den Nullstellen der Legendre-Polynome -- Chebyshev semi-discrete approximations for linear parabolic problems -- On the convergence theory of Padรฉ approximants -- Singular self-adjoint multipoint boundary value problems: Solutions and approximations -- ร{156}ber die Konvergenz von natรผrlichen interpolierenden Splines -- New and Unsolved Problems -- Alphabetical List of Papers

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