Linear Operators and Approximation / Lineare Operatoren Und Approximation : Proceedings of the Conference Held at the Oberwolfach Mathematical Research Institute, Black Forest, August 14–22, 1971 / Abhandlungen Zur Tagung Im Mathematischen Forschungsinsti

These proceedings contain the lectures presented at the Conference on Linear Operators and Approximation held at the Oberwolfach Mathematical Research In­ stitute, August 14-22, 1971. There were thirty-eight such lectures while four addi­ 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 non­ 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. Front Matter....Pages 1-17 Front Matter....Pages 19-19 Generalizations of Landau’s Inequality to Linear Operators....Pages 20-32 Semi-Groups of Nonlinear Transformations....Pages 33-53 Singular Perturbations of Semi-Group Generators....Pages 54-61 Cyclic Vectors and Commutants....Pages 62-67 Some Applications of Operator Valued Analytic Functions of Two Complex Variables....Pages 68-79 Weyl’s Theorems....Pages 80-93 Some Approximation Problems in the Theory of Stationary Processes....Pages 94-101 Ein Operatorenkalkül für das approximationstheoretische Verhalten des Ergodensatzes im Mittel....Pages 102-114 A Note on the Landau—Kallman—Rota—Hille Inequality....Pages 115-119 Front Matter....Pages 121-121 Representation Theorems for Riesz Spaces....Pages 122-128 Boundedness from Measure Theory....Pages 129-137 Exchange of Infinite Summation with Limits in Banach Spaces....Pages 138-141 Finite Parts of Distributions....Pages 142-158 Courants et courants cylindriques sur des variétés de dimension infinie....Pages 159-174 Subdefinite Functions....Pages 175-177 Eine Bemerkung zum Banachschen Fixpunktsatz....Pages 178-181 On a Certain Converse of Hölder’s Inequality....Pages 182-184 Front Matter....Pages 185-185 On Some Geometric Properties of the Unit Sphere....Pages 186-195 Diskrete Konvergenz linearer Operatoren III....Pages 196-216 On Set-Valued Metric Projections....Pages 217-233 Front Matter....Pages 185-185 On the Comparison of Approximation Processes in Hilbert Spaces....Pages 234-253 Sätze vom Jackson-Typ auf Darstellungsräumen kompakter, zusammenhängender Liegruppen....Pages 254-272 Approximation d’espaces de fonctions C ∞ et interpolation....Pages 273-280 Nonlinear Transformations with the Conservation of Differential Properties of Functions....Pages 281-283 Positive and Monotone Approximation....Pages 284-291 Sätze vom Bohman—Korowkin-Typ für Banachsche Funktionenräume....Pages 292-299 Front Matter....Pages 301-301 Projection métrique de L 1 ( T ) sur des sous-espaces fermés invariants par translation....Pages 302-309 Bases dans H et bases de sous espaces de dimension finie dans A ....Pages 310-324 Logarithmic and Exponential Variants of Bernstein’s Inequality and Generalized Derivatives....Pages 325-337 Fourier Multipliers whose Multiplier Norm is an Attained Value....Pages 338-347 Nikolskiĭ Constants for Positive Singular Integrals of Perturbed Fejér-Type....Pages 348-363 A Pointwise “ o ” Saturation Theorem for Positive Convolution Operators....Pages 364-370 Convolution Operators for Fourier—Jacobi Expansions....Pages 371-380 Front Matter....Pages 381-381 Cardinal Interpolation and Spline Functions IV. The Exponential Euler Splines....Pages 382-404 Применения сплайнов в теории приближений....Pages 405-418 The Fundamental Theorem of Algebra for Monosplines with Multiplicities....Pages 419-430 A Contribution to the Problem of Weighted Polynomial Approximation....Pages 431-447 Zur Konvergenz der Stufenpolynome über den Nullstellen der Legendre-Polynome....Pages 448-451 Chebyshev Semi-Discrete Approximations for Linear Parabolic Problems....Pages 452-460 On the Convergence Theory of Padé Approximants....Pages 461-469 Front Matter....Pages 381-381 Singular Self-Adjoint Multipoint Boundary Value Problems: Solutions and Approximations....Pages 470-486 Über die Konvergenz von natürlichen interpolierenden Splines....Pages 487-492 Back Matter....Pages 493-506 These proceedings contain the lectures presented at the Conference on Linear Operators and Approximation held at the Oberwolfach Mathematical Research InƯ stitute, August 14-22, 1971. There were thirty-eight such lectures while four addiƯ 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 nonƯ 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 Edited By P. L. Butzer, J.-p. Kahane, B. Szökefalvi-nagy.