Linear Spaces and Approximation / Lineare Räume Und Approximation : Proceedings of the Conference Held at the Oberwolfach Mathematical Research Institute, Black Forest, August 20–27,1977 / Abhandlungen Zur Tagung Im Mathematischen Forschungsinstitut Oberw

The publication of Oberwolfach conference books was initiated by Birkhauser Publishers in 1964 with the proceedings of the conference 'On Approximation Theory', conducted by P. L. Butzer (Aachen) and J. Korevaar (Amsterdam). Since that auspicious beginning, others of the Oberwolfach proceedings have appeared in Birkhauser's ISNM series. The present volume is the fifth \* edited at Aachen in collaboration with an external institution. It once again ad­ dresses itself to the most recent results on approximation and operator theory, and includes 47 of the 48 lectures presented at Oberwolfach, as well as five articles subsequently submitted by V. A. Baskakov (Moscow), H. Esser (Aachen), G. Lumer (Mons), E. L. Stark (Aachen) and P. M. Tamrazov (Kiev). In addition, there is a section devoted to new and unsolved problems, based upon two special problem sessions augmented by later communications from the participants. Corresponding to the nature of the conference, the aim of the organizers was to solicit both specialized and survey papers, ranging in the broad area of classical and functional analysis, from approximation and interpolation theory to Fourier and harmonic analysis, and to the theory of function spaces and operators. The papers were supplemented by lectures on fields represented for the first time in our series of Oberwolfach Conferences, so for example, complex function theory or probability and sampling theory. Front Matter....Pages 1-9 Zur Tagung....Pages 11-11 List of participants....Pages 13-15 Wissenschaftliches Programm....Pages 17-19 Front Matter....Pages 21-21 Kernel Operators....Pages 23-31 Invariant Operator Ranges....Pages 33-36 Diagonalization of Matrices over H ∞ ....Pages 37-46 Biquasitriangular Operators and Quasisimilarity....Pages 47-52 Applications of Transference: The L p Version of von Neumann’s Inequality and the Littlewood-Paley-Stein Theory....Pages 53-67 Front Matter....Pages 69-69 An Outline of Vector Graphs and Conditional Banach Spaces....Pages 71-89 The Exponential Map for Symmetric Operators in Spaces with an Indefinite Scalar Product....Pages 91-99 Nonarchimedean Function Spaces....Pages 101-117 Kodissipative Metrische Projektionen in Normierten Linearen Räumen....Pages 119-130 Front Matter....Pages 131-131 Recent Results and Unsolved Problems on Finite Convolution Operators....Pages 133-150 Weak-Type Inequalities in Analysis....Pages 151-162 Fractional Lipschitz Spaces Generated by Rearrangement-Invariant Norms....Pages 163-175 Some Inequalities for Fractional Integrals....Pages 177-184 Front Matter....Pages 185-185 Differentiation on a p-Adic Or p-Series Field....Pages 187-198 Remarks on the Kronecker’s Approximation Theorem and a Unitary Measure....Pages 199-202 Lebesgue Constants for Certain Partial Sums of Fourier Series on Compact Lie Groups....Pages 203-211 Real Function Methods in Fourier Analysis....Pages 213-227 Front Matter....Pages 185-185 Lipschitz Continuity of Spherical Means....Pages 229-234 Multiplier Representations of Sequence Spaces with Applications to Lipschitz Spaces and Spaces of Functions of Generalized Bounded Variation....Pages 235-245 Multipliers for the Mellin Transformation....Pages 247-249 On a Relation between the Norms of Cesaro Means of Jacobi Expansions....Pages 251-262 Front Matter....Pages 263-263 Approximation Et Analyse Harmonique....Pages 265-288 Estimations Involving a Modulus of Continuity for a Generalization of Korovkin’s Operators....Pages 289-303 Die Lokale L p — Saturationsklasse des Verfahrens der Integralen Meyer — König und Zeller Operatoren....Pages 305-317 Global Approximation Theorems for the Szász-Mirakjan Operators in Exponential Weight Spaces....Pages 319-333 Approximation With Monotonic Operators in A-Distance....Pages 335-341 Jackson’s Theorem for Polynomials and Exponential Sums with Restricted Coefficients....Pages 343-358 Birkhoff Quadrature Matrices....Pages 359-374 On some Problems in Interpolation Theory....Pages 375-380 Bivariate and Multivariate Interpolation with Noncommutative Projectors....Pages 381-387 Über Eine Hypothese von P.P. Korovkin....Pages 389-393 Front Matter....Pages 395-395 L p [-1, 1] Approximation by Algebraic Polynomials....Pages 397-406 Gewichtete Beste Approximation Stetiger Funktionen durch Algebraische Polynome....Pages 407-421 Erweiterung des Satzes von Markoff....Pages 423-431 Convergence of Spline Expansions....Pages 433-448 Direct and Converse Theorems for Oneside Approximation....Pages 449-458 Front Matter....Pages 459-459 Approximation von Ebenen Harmonischen Funktionen Durch Solche mit Wachstumsbeschränkung....Pages 461-469 Front Matter....Pages 459-459 Extreme Points of Spaces of Univalent Functions....Pages 471-477 Lacunary Polynomial Approximation....Pages 479-489 Müntz-Szasz Theorems and Lacunary Entire Functions....Pages 491-501 Structural and Approximational Properties of Functions in the Complex Domain....Pages 503-514 Front Matter....Pages 515-515 A Generalization of the Cauchy-Kowalevsky Theorem and Boundary Values of Solutions of Elliptic Equations....Pages 517-529 Lax-Type Theorems with Orders in Connection with Inhomogeneous Evolution Equations in Banach Spaces....Pages 531-546 Evolution Equations in Sup-Norm Context And in L 2 Variational Context....Pages 547-558 Zur Diskretisierung von Randwertaufgaben Gewöhnlicher Differentialgleichungen....Pages 559-567 Front Matter....Pages 569-569 Fourier Series and Martingale Transforms....Pages 571-581 Inverse Theorems on the Rate of Approximation for Certain Limit Theorems in Probability Theory....Pages 583-601 Maximal Inequalities and Convergence Properties of Multiple Orthogonal Series and Random Fields....Pages 603-614 Some Extensions of the Sampling Theorem....Pages 615-628 A Bibliography on the Approximation of Functions by Operators of Class S 2m or S m Involving Kernels of Finite Oscillations....Pages 629-639 A Survey of Some Results on Invariant Subspaces in Operator Theory....Pages 641-657 New and Unsolved Problems....Pages 659-671 Back Matter....Pages 673-685 The publication of Oberwolfach conference books was initiated by Birkhauser Publishers in 1964 with the proceedings of the conference 'On Approximation Theory', conducted by P.L. Butzer (Aachen) and J. Korevaar (Amsterdam). Since that auspicious beginning, others of the Oberwolfach proceedings have appeared in Birkhauser's ISNM series. The present volume is the fifth * edited at Aachen in collaboration with an external institution. It once again adƯ dresses itself to the most recent results on approximation and operator theory, and includes 47 of the 48 lectures presented at Oberwolfach, as well as five articles subsequently submitted by V.A. Baskakov (Moscow), H. Esser (Aachen), G. Lumer (Mons), E.L. Stark (Aachen) and P.M. Tamrazov (Kiev). In addition, there is a section devoted to new and unsolved problems, based upon two special problem sessions augmented by later communications from the participants. Corresponding to the nature of the conference, the aim of the organizers was to solicit both specialized and survey papers, ranging in the broad area of classical and functional analysis, from approximation and interpolation theory to Fourier and harmonic analysis, and to the theory of function spaces and operators. The papers were supplemented by lectures on fields represented for the first time in our series of Oberwolfach Conferences, so for example, complex function theory or probability and sampling theory