Linear spaces and approximation. Proceedings of the conference held at the Oberwolfach Mathematical Research Inst. Black Forest Aug. 20-27 1977 = Lineare Räume und Approximation.

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.

Zur Tagung.- List of participants.- Wissenschaftliches Programm.- I Operator Theory.- Kernel Operators.- Invariant Operator Ranges.- Diagonalization of Matrices over H?.- Biquasitriangular Operators and Quasisimilarity.- Applications of Transference: The Lp version of von Neumann’s Inequality and the Littlewood-Paley-Stein Theory.- II Topics in Functional Analysis.- An Outline of Vector Graphs and Conditional Banach Spaces.- The Exponential Map for Symmetric Operators in Spaces with an Indefinite Scalar Product.- Nonarchimedean Function Spaces.- Kodissipative metrische Projektionen in normierten linearen Räumen.- III Integral Operators and Inequalities.- Recent Results and Unsolved Problems on Finite Convolution Operators.- Weak-type Inequalities in Analysis.- Fractional Lipschitz Spaces Generated by Rearrangement-invariant Norms.- Some Inequalities for Fractional Integrals.- IV Harmonic Analysis.- Differentiation on a p-Adic or p-Series Field.- Remarks on Kronecker’s Approximation Theorem and a Unitary Measure.- Lebesgue Constants for Certain Partial Sums of Fourier Series on Compact Lie Groups.- Real Function Methods in Fourier Analysis.- Lipschitz Continuity of Spherical Means.- Multiplier Representations of Sequence Spaces with Applications to Lipschitz Spaces and Spaces of Functions of Generalized Bounded Variation.- Multipliers for the Mellin Transformation.- On a Relation Between the Norms of Cesàro Means of Jacobi Expansions.- V Approximation Processes and Interpolation.- Approximation et Analyse Harmonique.- Estimations Involving a Modulus of Continuity for a Generalization of Korovkin’s Operators.- Die lokale Lp-Saturationsklasse des Verfahrens der integralen Meyer-König und Zeller Operatoren.- Global Approximation Theorems for the Szász-Mirakjan Operators in Exponential Weight Spaces.- Approximation with Monotonic Operators in A-Distance.- Jackson’s Theorem for Polynomials and Exponential Sums with Restricted Coefficients.- Birkhoff Quadrature Matrices.- On Some Problems in Interpolation Theory.- Bivariate and Multivariate Interpolation with Noncommutative Projectors.- Über eine Hypothese von P.P. Korovkin.- VI Best Approximation and Splines.- Lp[-1, 1] Approximation by Algebraic Polynomials.- Gewichtete beste Approximation stetiger Funktionen durch algebraische Polynome.- Erweiterung des Satzes von Markoff.- Convergence of Spline Expansions.- Direct and Converse Theorems for Onesided Approximation.- VII Complex Function Theory and Approximation.- Approximation von ebenen, harmonischen Funktionen durch solche mit Wachstumsbeschränkung.- Extreme Points of Spaces of Univalent Functions.- Lacunary Polynomial Approximation.- Müntz-Szasz Theorems and Lacunary Entire Functions.- Structural and Approximational Properties of Functions in the Complex Domain.- VIII Differential Operators and Equations.- A Generalization of the Cauchy-Kowalevsky Theorem and Boundary Values of Solutions of Elliptic Equations.- Lax-type Theorems with Orders in Connection with Inhomogeneous Evolution Equations in Banach Spaces.- Evolution Equations in Sup-norm Context and in L2 Variational Context.- Zur Diskretisierung von Randwertaufgaben gewöhnlicher Differentialgleichungen.- IX Probability Theory and Other Applications.- Fourier Series and Martingale Transforms.- Inverse Theorems on the Rate of Approximation for Certain Limit Theorems in Probability Theory.- Maximal Inequalities and Convergence Properties of Multiple Orthogonal Series and Random Fields.- Some Extensions of the Sampling Theorem.- A Bibliography on the Approximation of Functions by Operators of Class S2m or Sm Involving Kernels of Finite Oscillations.- A Survey of Some Results on Invariant Subspaces in Operator Theory.- New and unsolved problems.- Alphabetical list of papers.- AMS (MOS) subject classification numbers.- Key words and phrases.