Gabor Szegö: Collected Papers

1945-1972
Softcover Nachdruck of the original 1. Auflage 1982
ISBN: 978-1-4612-5787-5
Verlag: Birkhäuser Boston

Buch, Englisch, 880 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 1641 g

Reihe: Contemporary Mathematicians

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".

Zielgruppe

Research

Autoren/Hrsg.

Szegö, Gabor P.

Inhaltsverzeichnis

— 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 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.