Gabor Szegö: Collected Papers
1945-1972
(Sprache: Englisch)
1. 1. Definition of L-forms. In the years 1907-1911 O. Toeplitz [21, 22, 23, 24] studied a class of quadratic forms whose matrix is of the follO\\"ing type: (Ll) C-2 C_I Co C-n-I Cn-I The elements Cn are given complex constants. Toeplitz designated these...
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1. 1. Definition of L-forms. In the years 1907-1911 O. Toeplitz [21, 22, 23, 24] studied a class of quadratic forms whose matrix is of the follO\\"ing type: (Ll) C-2 C_I Co C-n-I Cn-I The elements Cn are given complex constants. Toeplitz designated these forms as L-forms and investigated in detail their relation to the analytic function defined in a neighborhood of the unit circle by the Laurent series 2; C z", n = n - 00, . . . , 00; this series is assumed to be convergent in a certain circular ring rl I z I r2, rl 1 r2. It is obvious that these matrices are connected with the infinite cyclic group, just as the finite cyclic matrix CO CI C2 C Co CI n r (1. 2) Cn-I C Co n L. c, c, Co is associated with the finite cyclic group. The main result of Toeplitz is that the spectrum of the L-form is identical with the complex values the Laurent series assumes on the unit circle I z I = 1. 1. 2. Hermitian forms. The case C = en is of particular importance; the n matrix (1. 1) is in this case a Hermitian one and the associated Laurent series i8 represents a real function f(8) on the unit circle z = e , -'II" ~ 8 '11".
Inhaltsverzeichnis zu „Gabor Szegö: Collected Papers “
- Volume 3.- (1945-1) Inequalities for the Capacity of a Condenser (with G. Pólya).- (1945-2) On the Capacity of a Condenser.- (1948-1) On an Inequality of P. Turán Concerning Legendre Polynomials.- (1949-1) The Virtual Mass of Nearly Spherical Solids.- (1949-2) Virtual Mass and Polarization (with M. Schiffer).- (1950-1)Über eine Verallgemeinerung des Dirichletschen Integrals.- (1950-2) On Membranes and Plates.- (1950-3) Extremum Problems for Non-Negative Sine Polynomials (with W. W. Rogosinski).- (1950-4) Conformal Mapping of the Interior of an Ellipse onto a Circle.- (1950-5) On the Relative Extrema of Legendre Polynomials.- (1950-6) On Certain Special Sets of Orthogonal Polynomials.- (1951-1) Special Conformal Mappings (with L. Fejér).- (1951-2) Principal Frequency, Torsional Rigidity and Electrostatic Capacity.- (1952-1) On Certain Set Functions Defined by Extremum Properties in the Theory of Functions and in Mathematical Physics.- (1952-2) On Certain Hermitian Forms Associated with the Fourier Series of a Positive Function.- (1952-3) Conformal Mapping Related to Torsional Rigidity, Principal Frequency, and Electrostatic Capacity.- (1952-4) Recent Contributions of the Hungarian School to Conformal Mapping.- (1953-1) A Note on the Reciprocal of a Fourier Series (with A. Edrei).- (1953-2) On the Vibrations of a Clamped Plate.- (1953-3) Remark on the Preceding Paper of Charles Loewner.- (1953-4) On the Eigen-values of Certain Hermitian Forms (with M. Kac and W. L. Murdock).- (1954-1) Inequalities for Certain Eigenvalues of a Membrane of Given Area.- (1954-2) On Certain Mean Values of Polynomials (with A. Zygmund).- (1954-3) On the Singularities of Zonal Harmonic Expansions.- (1954-4) On a Theorem of C. Carathéodory.- (1954-5) Otto Szász.- (1954-6) Review of Higher Transcendental Functions, Vols. 1 and 2.- (1955-1) On Algebraic Equations with Integral Coefficients Whose Roots Belong to a Given Point Set (with M. Fekete).- (1955-2) On a Certain Kind of
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Symmetrization and Its Applications.- (1956-1) Relations between Different Capacity Concepts.- (1958-1) Note to My Paper "On Membranes and Plates".- (1959-1) Recent Advances and Open Questions on the Asymptotic Expansions of Orthogonal Polynomials.- (1960-1) On Certain Differential-Integral Equations (with S. Karlin).- (1960-2) Concerning the Fourier Coefficients of a Nonnegative Function.- (1960-3) A Problem in Prediction Theory (with Henry Helson).- (1960-4) Leopold Fejér: In Memoriam 1880-1959.- (1960-5) Emlékezés Fejér Lipótra.- (1960-6) An Extremum Problem for Polynomials (with I. J. Schoenberg).- (1960-7) On the Gradient of Solid Harmonic Polynomials.- (1960-8) On Certain Determinants Whose Elements are Orthogonal Polynomials (with S. Karlin).- (1961-1) On the Monotone Convergence of Certain Riemann Sums (with P. Turán).- (1962-1) On Positive Harmonic Polynomials.- (1962-2) An Inequality for Jacobi Polynomials.- (1963-1) On Bi-Orthogonal Systems of Trigonometric Polynomials.- (1963-2) On the Positivity of Certain Sums of Ultraspherical Polynomials, by Ervin Feldheim with a note by G. Szegö.- (1964-1) On a Problem of the Best Approximation.- (1964-2) On Some Problems of Approximations.- (1968-1) An Outline of the History of Orthogonal Polynomials.- (1972-1) The Contributions of L. Fejér to the Constructive Function Theory.
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Bibliographische Angaben
- Autor: Gabor P. Szegö
- 1982, 880 Seiten, Maße: 26 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 0817630619
- ISBN-13: 9780817630614
Sprache:
Englisch
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