Schoenberg, I. J.
Overview
Works:  145 works in 429 publications in 5 languages and 1,971 library holdings 

Roles:  Author, Editor 
Classifications:  QA7, 510 
Publication Timeline
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Most widely held works about
I. J Schoenberg
 Schoenberg, I.J., papers by I. J Schoenberg( )
 George Polya papers by George Pólya( )
Most widely held works by
I. J Schoenberg
Mathematical time exposures by
I. J Schoenberg(
Book
)
13 editions published between 1982 and 1989 in 3 languages and held by 473 WorldCat member libraries worldwide
13 editions published between 1982 and 1989 in 3 languages and held by 473 WorldCat member libraries worldwide
Approximations, with special emphasis on spline functions; proceedings of a symposium conducted by the Mathematics Research
Center, United States Army, at the University of Wisconsin, Madison, May 57, 1969 by
I. J Schoenberg(
Book
)
22 editions published between 1964 and 1969 in 3 languages and held by 435 WorldCat member libraries worldwide
22 editions published between 1964 and 1969 in 3 languages and held by 435 WorldCat member libraries worldwide
Cardinal spline interpolation by
I. J Schoenberg(
Book
)
32 editions published between 1973 and 1993 in English and Italian and held by 389 WorldCat member libraries worldwide
Annotation
32 editions published between 1973 and 1993 in English and Italian and held by 389 WorldCat member libraries worldwide
Annotation
Selected papers by
I. J Schoenberg(
Book
)
10 editions published in 1988 in English and Miscellaneous languages and held by 143 WorldCat member libraries worldwide
10 editions published in 1988 in English and Miscellaneous languages and held by 143 WorldCat member libraries worldwide
Selected papers by
I. J Schoenberg(
Book
)
6 editions published in 1988 in English and German and held by 35 WorldCat member libraries worldwide
6 editions published in 1988 in English and German and held by 35 WorldCat member libraries worldwide
Selected papers by
Isaac J Schoenberg(
Book
)
5 editions published in 1988 in English and German and held by 32 WorldCat member libraries worldwide
5 editions published in 1988 in English and German and held by 32 WorldCat member libraries worldwide
The Chinese Remainder Problem and Polynomial Interpolation by
I. J Schoenberg(
Book
)
8 editions published between 1985 and 1986 in English and Undetermined and held by 8 WorldCat member libraries worldwide
The Chinese Remainder Problem (Ch. R.P) is to find an integer x such that x = a sub i(mod m sub i) (i=1 ..., n), where mi are pairwise relatively prime moduli and a sub i are given integers. In the 1950's I learnt orally from Marcel Riesz that the CH. R.P. is an analogue of the polynomial interpolation problem P(x sub i) = Y sub i(i=1 ..., n), P(x) is a subset of pi sub n1, and that the Ch. R.P. can be solved by an analogue of Lagrange's interpolation formula. The author now adds the remark that the Ch. R.P. can be solved, even more economically, by an analogue of Newton formula using successive divided differences
8 editions published between 1985 and 1986 in English and Undetermined and held by 8 WorldCat member libraries worldwide
The Chinese Remainder Problem (Ch. R.P) is to find an integer x such that x = a sub i(mod m sub i) (i=1 ..., n), where mi are pairwise relatively prime moduli and a sub i are given integers. In the 1950's I learnt orally from Marcel Riesz that the CH. R.P. is an analogue of the polynomial interpolation problem P(x sub i) = Y sub i(i=1 ..., n), P(x) is a subset of pi sub n1, and that the Ch. R.P. can be solved by an analogue of Lagrange's interpolation formula. The author now adds the remark that the Ch. R.P. can be solved, even more economically, by an analogue of Newton formula using successive divided differences
On cardinal spline smoothing by
I. J Schoenberg(
Book
)
8 editions published between 1977 and 1979 in English and held by 8 WorldCat member libraries worldwide
The paper has two parts. In part I it describes the old results on the problem of smoothing a given biinfinite sequence of equidistant data. It includes the main results on the cardinal spline interpolation of equidistant data of power growth. All this is meant as background for the new developments in Part II. In Part II a method of smoothing a sequence of equidistant data is presented. It is based on the ideas of E.T. Whittaker
8 editions published between 1977 and 1979 in English and held by 8 WorldCat member libraries worldwide
The paper has two parts. In part I it describes the old results on the problem of smoothing a given biinfinite sequence of equidistant data. It includes the main results on the cardinal spline interpolation of equidistant data of power growth. All this is meant as background for the new developments in Part II. In Part II a method of smoothing a sequence of equidistant data is presented. It is based on the ideas of E.T. Whittaker
Hausdorff's moment problem and expansions in Legendre polynomials by
Richard Askey(
Book
)
5 editions published between 1980 and 1981 in English and held by 7 WorldCat member libraries worldwide
A new proof is given for Hausdorff's condition on a set of moments which determines when the function generating these moments is in L2. The proof uses Legendre polynomials and their discrete extensions found by Tchebychef. Then an extension is given to a weighted L2 space using Jacobi polynomials and their discrete extensions. (Author)
5 editions published between 1980 and 1981 in English and held by 7 WorldCat member libraries worldwide
A new proof is given for Hausdorff's condition on a set of moments which determines when the function generating these moments is in L2. The proof uses Legendre polynomials and their discrete extensions found by Tchebychef. Then an extension is given to a weighted L2 space using Jacobi polynomials and their discrete extensions. (Author)
The Landau problem for motions in a ring and in bounded continua by
I. J Schoenberg(
Book
)
6 editions published in 1975 in English and held by 6 WorldCat member libraries worldwide
6 editions published in 1975 in English and held by 6 WorldCat member libraries worldwide
On polynomial interpolation in the points of a geometric progression, Stirling, Schellbach, Runge and Romberg by
I. J Schoenberg(
Book
)
4 editions published in 1981 in English and held by 6 WorldCat member libraries worldwide
It is very well known Newton's interpolation series with divided differences simplifies considerably in the case that we interpolate in the points of an arithmetic progression. It seems much less known that a similar simplification occurs in the case when the points of interpolation form a geometric progression. We describe here the practically forgotten work of Stirling (1730), Schellbach) (1864), and Runge (1981), and its connection with the elegant and more recent algorithm of Romberg (1955). (Author)
4 editions published in 1981 in English and held by 6 WorldCat member libraries worldwide
It is very well known Newton's interpolation series with divided differences simplifies considerably in the case that we interpolate in the points of an arithmetic progression. It seems much less known that a similar simplification occurs in the case when the points of interpolation form a geometric progression. We describe here the practically forgotten work of Stirling (1730), Schellbach) (1864), and Runge (1981), and its connection with the elegant and more recent algorithm of Romberg (1955). (Author)
On semicardinal quadrature formulae by
I. J Schoenberg(
Book
)
5 editions published in 1973 in English and held by 6 WorldCat member libraries worldwide
The present paper concerns the semicardinal quadrature formulae introduced in a previous paper. These were the limiting forms of Sard's best quadrature formulae as the number of nodes increases indefinitely. Here the authors give a new derivation and characterization of these formulae. This derivation uses appropriate generating functions and also allows to compute the coefficients very accurately. (Author)
5 editions published in 1973 in English and held by 6 WorldCat member libraries worldwide
The present paper concerns the semicardinal quadrature formulae introduced in a previous paper. These were the limiting forms of Sard's best quadrature formulae as the number of nodes increases indefinitely. Here the authors give a new derivation and characterization of these formulae. This derivation uses appropriate generating functions and also allows to compute the coefficients very accurately. (Author)
Two applications of approximate differentiation formulae : an extremum problem for multiply monotone functions and the differentiation
of asymptotic expansions by
I. J Schoenberg(
Book
)
5 editions published in 1980 in English and held by 6 WorldCat member libraries worldwide
This report presents two further applications of very elementary formulae of approximate differentiation. The first is a new derivation in a somewhat sharper form of a theorem of V.M. Olovyanisnikov on multiply monotone functions. The second applications gives sufficient conditions for the differentiability of asymptotic expansions
5 editions published in 1980 in English and held by 6 WorldCat member libraries worldwide
This report presents two further applications of very elementary formulae of approximate differentiation. The first is a new derivation in a somewhat sharper form of a theorem of V.M. Olovyanisnikov on multiply monotone functions. The second applications gives sufficient conditions for the differentiability of asymptotic expansions
The Elementary Cases of Landau's Problem of Inequalities Between Derivatives by
I. J Schoenberg(
Book
)
5 editions published between 1971 and 1972 in English and held by 5 WorldCat member libraries worldwide
The paper covers those cases of Landau's problem that are accessible by using only methods of elementary Calculus. A novel contribution of the paper, besides the proofs, is the discussion of the extremizing functions. (Author)
5 editions published between 1971 and 1972 in English and held by 5 WorldCat member libraries worldwide
The paper covers those cases of Landau's problem that are accessible by using only methods of elementary Calculus. A novel contribution of the paper, besides the proofs, is the discussion of the extremizing functions. (Author)
On Chebyshev and Markovtype problems for polynomials in circular ring by
I. J Schoenberg(
Book
)
6 editions published in 1975 in English and held by 5 WorldCat member libraries worldwide
6 editions published in 1975 in English and held by 5 WorldCat member libraries worldwide
The Bsplines for cardinal Hermite interpolation by
I. J Schoenberg(
Book
)
5 editions published in 1971 in English and held by 5 WorldCat member libraries worldwide
The paper is devoted to a study of the Bsplines for the problem of cardinal Hermite interpolation by spline functions. (Author)
5 editions published in 1971 in English and held by 5 WorldCat member libraries worldwide
The paper is devoted to a study of the Bsplines for the problem of cardinal Hermite interpolation by spline functions. (Author)
The finite Fourier series : II, the harmonic analysis of skew polyons as a source of outdoor sculptures by
I. J Schoenberg(
Book
)
4 editions published in 1979 in English and held by 5 WorldCat member libraries worldwide
The subject of the finite Fourier series and some new applications to problems of elementary geometry are applied to a theorem of Jesse Douglas on skew pentagons in space. It is shown here that Douglas' theorem amounts to the graphical harmonic analysis of skew pentagons and that it is also the source of striking outdoor sculptures. (Author)
4 editions published in 1979 in English and held by 5 WorldCat member libraries worldwide
The subject of the finite Fourier series and some new applications to problems of elementary geometry are applied to a theorem of Jesse Douglas on skew pentagons in space. It is shown here that Douglas' theorem amounts to the graphical harmonic analysis of skew pentagons and that it is also the source of striking outdoor sculptures. (Author)
Splines and the logarithmic function by
Donald J Newman(
Book
)
6 editions published in 1974 in English and held by 5 WorldCat member libraries worldwide
Let q be fixed, q>1, and let f(x) = log x/log q in (0, pos infinity). The paper determines the unique spline function (S sub n)(x), of degree n, defined in (0, pos infinity) and having as knots the points of the sequence (q sup nu) (neg infinity <nu <infinity), such as to satisfy the conditions (S sub n)(qx) = (Sub n)(x) + 1 if x>0, and (S sub n)(1) = 0. It follows that (S sub n)(q nu) = f(q sup nu) for all integers nu. It is shown that (S sub n)(x) shares with f(x) its monotonicity properties of hither order. Nevertheless and against all expectations it is shown that (S sub n)(x) does not converge to f(x) as n nears infinity. Most of the paper is devoted to an analysis of the peculiar asymptotic behavior of (S sub n)(x)
6 editions published in 1974 in English and held by 5 WorldCat member libraries worldwide
Let q be fixed, q>1, and let f(x) = log x/log q in (0, pos infinity). The paper determines the unique spline function (S sub n)(x), of degree n, defined in (0, pos infinity) and having as knots the points of the sequence (q sup nu) (neg infinity <nu <infinity), such as to satisfy the conditions (S sub n)(qx) = (Sub n)(x) + 1 if x>0, and (S sub n)(1) = 0. It follows that (S sub n)(q nu) = f(q sup nu) for all integers nu. It is shown that (S sub n)(x) shares with f(x) its monotonicity properties of hither order. Nevertheless and against all expectations it is shown that (S sub n)(x) does not converge to f(x) as n nears infinity. Most of the paper is devoted to an analysis of the peculiar asymptotic behavior of (S sub n)(x)
Extremum problems for the motions of a billiard ball : IV. A higherdimensional analogue of Kepler's stella octangula by
I. J Schoenberg(
Book
)
4 editions published in 1980 in English and held by 5 WorldCat member libraries worldwide
Let us consider a square billiard table gamma 2 = ABCD, and let A'B'C'D' be a concentric square half the size of ABCD. Let alpha, beta, gamma, delta, be the midpoints of the sides of gamma 2. We observe that the path of a billiard ball moving along the sides of the square alpha beta gamma delta does not penetrate inside the square A'B'C'D'. However, it can be shown that the path of any other billiard ball must penetrate into the square A'B'C'D'. By 'any other' we mean (1) That the path is not parallel to any side of gamma 2. (2) That the path is different from alpha beta gamma delta. In the present paper this curious property of plane billiard ball motions is extended to a certain class of skew polytopes in the ndimensional space R superscript n. These polytopes reduce to plane billiard ball motions if n = 2. If n = 3 the above property of the square alpha beta gamma delta is taken over by Kepler's Stella Octangula. This is an 8pointed star which is explained in the paper
4 editions published in 1980 in English and held by 5 WorldCat member libraries worldwide
Let us consider a square billiard table gamma 2 = ABCD, and let A'B'C'D' be a concentric square half the size of ABCD. Let alpha, beta, gamma, delta, be the midpoints of the sides of gamma 2. We observe that the path of a billiard ball moving along the sides of the square alpha beta gamma delta does not penetrate inside the square A'B'C'D'. However, it can be shown that the path of any other billiard ball must penetrate into the square A'B'C'D'. By 'any other' we mean (1) That the path is not parallel to any side of gamma 2. (2) That the path is different from alpha beta gamma delta. In the present paper this curious property of plane billiard ball motions is extended to a certain class of skew polytopes in the ndimensional space R superscript n. These polytopes reduce to plane billiard ball motions if n = 2. If n = 3 the above property of the square alpha beta gamma delta is taken over by Kepler's Stella Octangula. This is an 8pointed star which is explained in the paper
On remainders and the convergence of cardinal spline interpolation for almost periodic functions by
I. J Schoenberg(
Book
)
6 editions published in 1974 in English and held by 5 WorldCat member libraries worldwide
It is shown that cardinal spline interpolation of degree 2m1 converges, as m nears infinity, for a certain class of almost periodic functions
6 editions published in 1974 in English and held by 5 WorldCat member libraries worldwide
It is shown that cardinal spline interpolation of degree 2m1 converges, as m nears infinity, for a certain class of almost periodic functions
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Related Identities
 Mathematics Research Center (United States. Army)
 University of Wisconsin
 De Boor, Carl Author Editor
 WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
 Society for Industrial and Applied Mathematics
 Conference Board of the Mathematical Sciences
 Boor, Carl de Editor
 University of WisconsinMadison Mathematics Research Center
 Sharma, A.
 United States Army Mathematics Research Center (Madison)
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Associated Subjects
Almost periodic functions Approximation theory Asymptotic expansions Bernays, Paul, Bieberbach, Ludwig, Bohr, Harald August, Borel, Emile, Brentano, Franz, CurvesRectification and quadrature De Finetti, Bruno Erdős, Paul, Fourier transformations Frege, Gottlob, Haar, Alfréd, Hadamard, Jacques, Harary, Frank Harmonic analysis Hilbert, David, Hille, Einar, Hurwitz, Adolf, Inequalities (Mathematics) Interpolation Jacobi polynomials Knuth, Donald Ervin, Landau, Edmund, Legendre's polynomials Lehmer, D. H.(Derrick Henry), Logarithmic functions Mathematics MathematicsStudy and teaching Monotonic functions Montel, Paul, Numerical analysisAcceleration of convergence Numerical differentiation Pfluger, Albert, Polygons Pringsheim, Alfred, Runge, Carl, Schoenberg, I. J Schur, Issai, Sierpinski, Waclaw, Sommerfeld, Arnold, Spline theory Stanford University.Department of Mathematics Stern, Alfred Szegő, Gábor, Universities and collegesFaculty Variational principles Vector spaces Weyl, Hermann,
Alternative Names
Isaac Iacobus Schoenberg
Isaac Jacob Schoenberg American mathematician
Isaac Jacob Schoenberg Matemático estadounidense de origen rumano
Isaac Jacob Schoenberg matematico rumeno
Isaac Jacob Schoenberg mathématicien américain
Isaac Jacob Schoenberg rumänischer Mathematiker, Entdecker der Splines
Isaac Jacob Schoenberg wiskundige uit Roemenië (19031990)
Schoenberg, I. J.
Schoenberg, I. J. 19031990
Schoenberg, Isaac J.
Schoenberg, Isaac Jacob 19031990
Schoenberg, Iso
Шёнберг, Исаак
ایزاک یاکوب شونبرگ ریاضیدان رومانییی
シェーンベルグ, I. J.
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