Mathematics from Leningrad to Austin: George G. Lorentz' Selected Works in Real, Functional and Numerical Analysis Volume 1

ISBN-13: 9781461253259 / Angielski / Miękka / 2011 / 548 str.

Rudolph A. Lorentz

Opis

This "Select a" contains approximately two thirds of the papers my 1932 to 1994. These papers are divided into four fields. father wrote from The first volume contains the papers on 1) Summability and Number Theory and 2) Interpolation. The second volume contains the fields 3) Real and Functional Analysis and 4) Approximation Theory. Each of these four groups of papers is introduced by a review of the contents and significance, respectively of the impact of these papers. The first volume contains, in addition, an autobiography, a complete list of publications, a list of doctoral students and four unpublished essays on mathematics in general: a) A report on the University of Leningrad b) On the work of the mathematical mind c) Proofs in Mathematics d) About Mathematical books. The report on the University of Leningrad, written in the late '40's, is a unique historical document which is still of current interest for several reasons. It is of interest for professional reasons since it contains a com- plete description of a mathematics majors' curriculum through his entire course of studies. From it one can see both the changes and invariants of course material as well as the students' course load. Then one can also see the consequences of admittedly extreme political intervention in uni- versity affairs. Today we use the term "politically correct," but in those times being politically correct was a matter of life and death.

Spis treści

— Volume 1.- Mathematics in a Broader Perspective (unpublished papers).- A Report on the University of Leningrad.- On the Work of the Mathematical Mind.- Proofs in Mathematics.- Writing Mathematical Books.- I. Summability and Number Theory.- G.G. Lorentz and the Theory of Summability.- [1] Über lineare Summierungsverfahren.- [8] Beziehungen zwischen den Umkehrsatzen der Limitierungstheorie.- [10] Über Limitierungsverfahren, die von einem Stieltjes-Integral abhangen.- [11] Eine Bemerkung über Limitierungsverfahren, die nicht schwächer als ein Cesàro-Verfahren sind.- [12] Fourier-Koeffizienten und funktionklassen.- [14] Tauberian theorems and Tauberian conditions.- [17] A contribution to the theory of divergent sequences.- [22] Direct theorems on methods of summability.- [23] (with K. Knoop) Beiträge zur absoluten.- [28] Direct theorems on methods of summability.- [29] Riesz methods of summation and orthogonal series.- [31] (with M.S. Macphail) Unbounded operators and a theorem of A. Robinson.- [33] Multiplicity of representation of integers by sums of elements of two given sets.- [36] (with A.G. Robinson) Core-consistency and total inclusion for methods of summability.- [37] Tauberian theorems for absolute summability.- [38] On a problem of additive number theory.- [39] Borel and Banach properties of methods of summation.- [42] (with K.L Zeller) Über Paare von limitierungsverfahren.- [43] (with K.L Zeller) Series rearrangements and analytic sets.- [44] (with P. Erdös) On the probability that n and g(n) are relatively prime.- [45] (with B.J. Eisenstadt) Boolean rings and Banach lattices.- [54] (with K.L. Zeller) Strong and ordinary summability.- [56] (with K.L. Zeller) Summation of sequences and series.- [80] (with K.L. Zeller) o-but not O-Tauberian theorems.- II. Interpolation.- The work of G.G. Lorentz on Birkhoff interpolation.- [76] Birkhoff approximation and the problem of free matrices.- [82] The Birkhoff interpolation theorem: New methods and results.- [84] (with K.L Zeller) Birkhoff interpolation problem; coalescence of rows.- [85] Zeros of splines and Birkhoff’s kernel.- [88] Independant knots in Birkhoff’s interpolation.- [91] Coalescence of matrices, regularity and singularity of Birkhoff interpolation problems.- [94] (with S.D. Riemenschneider) Birkhoff quadrature matrices.- [95] Symmetry in Birkhoff matrices.- [97] (with S.D. Riemenschneider) Probabilistic approach to Schoenberg’s problem in Birkhoff interpolation.- [99] (with S.D. Riemenschneider) Birkhoff interpolation: some applications of coalescence.- [102] Independent sets of knots and singularity of interpolation matrices.- [103] (with R.A. Lorentz) Probability and interpolation.- [104] (with N. Dyn and S.D. Riemenschneider) Continuity of the Birkhoff interpolation.- [105] The analytic character of the Birkhoff interpolation polynomials.- [109] (with K. Jetter and S.D. Riemenschneider) Rolle theorem in spline interpolation.- [114] (with R.A. Lorentz) Multivariate interpolation.- [116] (with R.A. Lorentz) Solvability problems of bivariate interpolation.- [117] Classic interpolation by polynomials in two variables.- [118] (with R.A. Lorentz) Solvability problems of bivariate approximation II: Applications.- [122] Solvability of multivariate interpolation.- [124] Notes on approximation.- [126] (with R.A. Lorentz) Bivariate Hermite interpolation and application to algebraic geometry.