# Isaac Jacob Schoenberg

American mathematician

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Mathematics

## Isaac Jacob Schoenberg's Degrees

- PhD Mathematics University of Vienna

## Why Is Isaac Jacob Schoenberg Influential?

(Suggest an Edit or Addition)According to Wikipedia, Isaac Jacob Schoenberg was a Romanian-American mathematician, known for his invention of splines. Life and career Schoenberg was born in Galați to a Jewish family, the youngest of four children. He studied at the University of Iași, receiving his M.A. in 1922. From 1922 to 1925 he studied at the Universities of Berlin and Göttingen, working on a topic in analytic number theory suggested by Issai Schur. He presented his thesis to the University of Iași, obtaining his Ph.D. in 1926. In Göttingen, he met Edmund Landau, who arranged a visit for Schoenberg to the Hebrew University of Jerusalem in 1928. During this visit, Schoenberg began his work on total positivity and variation-diminishing linear transformations. In 1930, he returned from Jerusalem, and married Landau's daughter Charlotte in Berlin.

## Isaac Jacob Schoenberg's Published Works

### Published Works

- The Integrability of Certain Functions and Related Summability Methods (1959) (1004)
- Metric spaces and completely monotone functions (1938) (990)
- Metric spaces and positive definite functions (1938) (828)
- Contributions to the Problem of Approximation of Equidistant Data by Analytic Functions (1988) (787)
- Contributions to the problem of approximation of equidistant data by analytic functions. Part A. On the problem of smoothing or graduation. A first class of analytic approximation formulae (1946) (771)
- The Relaxation Method for Linear Inequalities (1954) (526)
- Remarks to Maurice Frechet's Article ``Sur La Definition Axiomatique D'Une Classe D'Espace Distances Vectoriellement Applicable Sur L'Espace De Hilbert (1935) (477)
- On Pólya frequency functions IV: The fundamental spline functions and their limits (1966) (436)
- Cardinal Spline Interpolation (1987) (419)
- Contributions to the problem of approximation of equidistant data by analytic functions. Part B. On the problem of osculatory interpolation. A second class of analytic approximation formulae (1946) (416)
- SPLINE FUNCTIONS AND THE PROBLEM OF GRADUATION. (1964) (378)
- Cardinal interpolation and spline functions (1969) (340)
- Positive definite functions on spheres (1942) (338)
- ON POLYA FREQUENCY FUNCTIONS. III. THE POSITIVITY OF TRANSLATION DETERMINANTS WITH AN APPLICATION TO THE INTERPOLATION PROBLEM BY SPLINE CURVES( (1953) (221)
- On Certain Metric Spaces Arising From Euclidean Spaces by a Change of Metric and Their Imbedding in Hilbert Space (1937) (212)
- On the generating functions of totally positive sequences I (1951) (200)
- Remarks on de la Vallée Poussin means and convex conformal maps of the circle. (1958) (161)
- On Pólya Frequency Functions (1988) (154)
- Fourier integrals and metric geometry (1941) (135)
- Über variationsvermindernde lineare Transformationen (1930) (134)
- On Hermite-Birkhoff interpolation☆ (1966) (133)
- On Polya frequency functions (1951) (121)
- SPLINE FUNCTIONS AND THE PROBLEM OF GRADUATION (1964) (108)
- Über die asymptotische Verteilung reeller Zahlen mod 1 (1928) (101)
- On Linear Functional Operations and the Moment Problem for a Finite Interval in One or Several Dimensions (1933) (88)
- Cardinal interpolation and spline functions: II interpolation of data of power growth (1972) (78)
- The Finite Fourier Series and Elementary Geometry (1950) (70)
- On smoothing operations and their generating functions (1953) (68)
- SOLUTION OF LANDAU'S PROBLEM CONCERNING HIGHER DERIVATIVES ON THE HALFLINE. (1970) (67)
- On Totally Positive Functions, LaPlace Integrals and Entire Functions of the LaGuerre-Polya-Schur Type. (1947) (64)
- A remark on M. M. Day’s characterization of inner-product spaces and a conjecture of L. M. Blumenthal (1952) (63)
- Spline Interpolation and Best Quadrature Formulae (1964) (60)
- On Euclidean Sets Having Only Two Distances Between Points. II (1966) (60)
- On Monosplines of Least Deviation and Best Quadrature Formulae (1965) (59)
- On the Zeros of the Generating Functions of Multiply Positive Sequences and Functions (1955) (58)
- On Best Approximations of Linear Operators (1964) (56)
- Notes on spline functions III: On the convergence of the interpolating cardinal splines as their degree tends to infinity (1973) (56)
- A note on the cyclotomic polynomial (1964) (55)
- The Elementary Cases of Landau's Problem of Inequalities Between Derivatives (1973) (54)
- Spline functions, convex curves and mechanical quadrature (1958) (53)
- Cardinal interpolation and spline functions. III. Cardinal Hermite interpolation (1973) (51)
- Regular Simplices and Quadratic Forms (1937) (51)
- On Variation Diminishing Spline Approximation Methods (1988) (50)
- SPLINE INTERPOLATION AND THE HIGHER DERIVATIVES. (1964) (50)
- On Monosplines of Least Square Deviation and Best Quadrature Formulae II (1966) (47)
- A remark on the preceding note by Bochner (1934) (46)
- On the Peano curve of Lebesgue (1938) (45)
- Splines and Histograms (1973) (45)
- On Interpolation by Spline Functions and its Minimal Properties (1988) (45)
- On the Ahlberg-Nilson extension of spline interpolation: The g-splines and their optimal properties☆ (1968) (45)
- Cardinal Interpolation and Spline Functions VIII. The Budan-Fourier Theorem for Splines and Applications. (1976) (43)
- On Pólya frequency functions. II: Variation-diminishing integral operators of the convolution type (1988) (39)
- On asymptotic distributions of arithmetical functions (1936) (39)
- An isoperimetric inequality for closed curves convex in even-dimensional euclidean spaces (1954) (39)
- On certain two-point expansions of integral functions of exponential type (1936) (37)
- On variation diminishing transformations on the circle (1959) (35)
- Cardinal Interpolation and Spline Functions IV. The Exponential Euler Splines (1972) (33)
- On semicardinal quadrature formulae (1974) (32)
- On a Theorem of Kirzbraun and Valentine (1953) (31)
- On Cauchy's Lemma Concerning Convex Polygons (1967) (30)
- Zur Abzählung der reellen Wurzeln algebraischer Gleichungen (1934) (30)
- On Variation-Diminishing Integral Operators of the Convolution Type. (1948) (30)
- Cardinal interpolation and spline fucntions V. The B-splines for cardinal Hermite interpolation (1973) (30)
- On the unicity of solutions of problems of best approximation (1961) (30)
- Notes on spline functions I. The limits of the interpolating periodic spline functions as their degree tends to infinity (1972) (29)
- On Metric Arcs of Vanishing Menger Curvature (1940) (29)
- Helly's Theorems on Convex Domains and Tchebycheff's Approximation Problem (1950) (29)
- A Conjectured Analogue of Rolle's Theorem for Polynomials with Real or Complex Coefficients (1986) (28)
- On polynomial interpolation at the points of a geometric progression (1981) (27)
- On spline interpolation at all integer points of the real axis (1968) (26)
- An extremum problem for polynomials (1960) (25)
- On the Besicovitch-Perron Solution of the Kakeya Problem (1988) (24)
- Hausdorff's moment problem and expansions in Legendre polynomials☆ (1982) (23)
- 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 5-7, 1969 (1969) (22)
- A second look at approximate quadrature formulae and spline interpolation (1970) (22)
- Cardinal interpolation and spline functions VI. Semi-cardinal interpolation and quadrature formulae (1974) (21)
- Notes on spline functions IV: A cardinal spline analogue of the theorem of the brothers Markov (1973) (20)
- Cardinal interpolation and spline functions VII. The behavior of cardinal spline interpolants as their degree tends to infinity (1974) (20)
- The perfectB-splines and a time-optimal control problem (1971) (19)
- On Jordan ARCS and Lipschitz classes of functions defined on them (1961) (17)
- On the Zeros of the Successive Derivatives of Integral Functions. (1935) (17)
- Some Applications of the Calculus of Variations to Riemannian Geometry (1932) (16)
- On cardinal monosplines of leastL∞-norm on the real axis (1970) (15)
- On Jacobi-Bertrand’s proof of a Theorem of Poncelet (1983) (15)
- Notes on spline functions V. Orthogonal or Legendre splines (1975) (14)
- Remarks concerning a numerical inversion of the Laplace transform due to Bellman, Kalaba, and Lockett (1973) (14)
- On finite-rowed systems of linear inequalities in infinitely many variables. II (1932) (14)
- On a conjecture concerning Schlicht functions (1959) (12)
- On equidistant cubic spline interpolation (1971) (12)
- On the maxima of certain hankel determinants and the zeros of the classical orthogonal polynomials (1959) (11)
- On Separation, Comparison and Oscillation Theorems for Self-Adjoint Systems of Linear Second Order Differential Equations (1931) (11)
- A brief account of my life and work (1988) (11)
- On the Remainders and the Convergence of Cardinal Spline Interpolation for Almost Periodic Functions (1988) (11)
- On finite and infinite completely monotonic sequences (1932) (11)
- The interpolatory background of the Euler-MacLaurin quadrature formula (1971) (11)
- Extremum problems for the motions of a billiard ball II. The L∞ norm☆ (1976) (11)
- A new approach to Euler splines (1983) (10)
- Extremum Problems for the Motions of a Billiard Ball. III. The Multi-Dimensional Case of Koenig and Szuecs. (1978) (10)
- Splines and the logarithmic function. (1975) (10)
- A Triangle Inequality (1977) (9)
- ON THE QUESTION OF UNICITY IN THE THEORY OF BEST APPROXIMATION (1960) (9)
- A note on multiply positive sequences and the Descartes rule of signs (1955) (8)
- ON THE USE OF SPLINE FUNCTIONS FOR THE APPROXIMATION OF SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS. (1967) (8)
- The spline interpolation of sequences satisfying a linear recurrence relation (1976) (7)
- On a theorem of szegö on univalent convex maps of the unit circle (1984) (6)
- Interpolating splines as limits of polynomials (1983) (6)
- On two theorems of P. Erdös and A. Rényi (1962) (6)
- On Semi-Cardinal Quadrature Formulae. (1973) (6)
- On local convexity in Hilbert space (1942) (5)
- The Chinese Remainder Problem and Polynomial Interpolation. (1987) (5)
- Convex domains and linear combinations of continuous functions (1933) (5)
- The Landau problem I.: The case of motions on sets (1978) (5)
- On lineal entire functions of $n$ complex variables (1952) (5)
- On Polynomial Spline Functions on the Circle 2. Monosplines and Quadrature Formulae (1971) (4)
- Two applications of approximate differentiation formulae: An extremum problem for multiply monotone functions and the differentiation of asymptotic expansions☆ (1982) (4)
- Arithmetic problems concerning cauchy's functional equation II (1964) (4)
- Some extremal problems for positive definite sequences and related extremal convex conformal maps of the circle (1958) (4)
- Linkages and distance geometry: II. On sets of n+2 points in En that are most nearly equilateral (1969) (4)
- On The Kakeya Constant (1965) (4)
- A Proof of Brace's Theorem by Induction. (1985) (3)
- Arithmetic problems concerning Cauchy's functional equation (1964) (3)
- N-Dimensional Volume (Maurice Eisenstein And M. S. Klamkin) (1960) (3)
- Uber total monotone Folgen mit stetiger Belegungsfunktlon (1929) (3)
- On a Problem of Steinhaus on Lattice Points (1979) (3)
- On the Location of the Frets on the Guitar. (1976) (3)
- Extensions of theorems of Descartes and Laguerre to the complex domain (1936) (3)
- The Landau problem I (1978) (2)
- EXTREMA FOR GAP POWER SERIES OF POSITIVE REAL PART. (1962) (2)
- The Landau Problem for Motions in a Ring and in Bounded Continua (1977) (2)
- 2. The Basis Property of B-Splines (1973) (2)
- The Landau problem. II. The case of motions on curves (1981) (2)
- High Order Continuity Implies Good Approximations to Solutions of Certain Functional Equations. (1981) (2)
- Norm inequalities for a certain class of ∞ functions (1971) (2)
- Publications of Edmund Landau (1969) (2)
- On the derivation of necessary conditions for the problem of Bolza (1932) (2)
- An iteration method for calculation with Laurent series (1946) (2)
- [60–6] An Extremum Problem for Polynomials (1982) (2)
- On the Matrix Approach to Fibonacci Numbers and the Fibonacci Pseudoprimes. (1977) (1)
- On Cardinal Spline Smoothing (1979) (1)
- The Landau Problem for Motions on Curves. (1977) (1)
- Extremum Problems for the Motions of a Billiard Ball. IV. A Higher-Dimensional Analogue of Kepler's Stella Octangula. (1980) (1)
- On Cardinal Monosplines of Least L sub infinity -Norm on the Real Axis. (1970) (1)
- A Direct Approach to the Villarceau Circles of a Torus. (1984) (1)
- The Minimizing Properties of Geodesic Arcs with Conjugate End Points (1931) (1)
- Cardinal spline interpolation and the exponential Euler splines (1974) (1)
- On the Equidecomposability of a Regular Triangle and A Square of Equal Areas. (1984) (1)
- Euler’s contribution to cardinal spline interpolation: The exponential Euler splines (1983) (1)
- Approximating Lengths, Areas and Volumes by Polygons and Polyhedra. (1976) (1)
- On the Anti-Cylinder. (1985) (0)
- On Vector Indices mod m (1988) (0)
- 6. Other Spaces and Semi-Cardinal Interpolation (1973) (0)
- 5. Cardinal Hermite Interpolation (1973) (0)
- On Hypocycloids and their Diameters (1985) (0)
- On Polynomial Interpolation in the Points of a Geometric Progression, Stirling, Schellbach, Runge and Romberg. (1981) (0)
- Norm Inequalities for a Certain Class of C∞ Functions (1988) (0)
- A Direct Derivation of a Jacobian Identity from Elliptic Functions (1981) (0)
- On the Turning Lozange of Constant Side Whose Vertices Alternate between Two Fixed Circles of a Ring. (1985) (0)
- On the Quadratic Mean Radius of a Polynomial in C(z). (1984) (0)
- The Harmonic Analysis of Skew Polygons as a Source of Outdoor Sculptures (1981) (0)
- Unique Prime Factorization and Lattice Points (1973) (0)
- 8. Semi-Cardinal Interpolation and Quadratures with General Boundary Conditions (1973) (0)
- Extremum problems for mass-distributions in a finite interval (1964) (0)
- 10. Applications: 1. Approximations of Fourier Transforms. 2. The Smoothing of Histograms (1973) (0)
- The Finite Fourier Series II. The Harmonic Analysis of Skew Polyons as a Source of Outdoor Sculptures. (1979) (0)
- 3. The Exponential Euler Splines (1973) (0)
- On the Theory and Practice of Multi-Dim. Indices mod m. A Circular Slide-Rule for the Modulus m = 100. (1986) (0)
- 7. Finite Spline Interpolation Problems (1973) (0)
- Extrema for gap power series of positive real part (1965) (0)
- 9. Extremum and Limit Properties (1973) (0)
- Self-reflecting skew polygons and polytopes in the 4-dimensional hypercube (1983) (0)
- On Fejer sets in linear and spherical spaces (1952) (0)
- On the Spans of Polynomials and the Spans of a Laguerre-Polya-Schur Sequence of Polynomials. (1984) (0)
- Piecewise smooth solutions of some difference-differential equations (1986) (0)
- The Landau problem. III. Motions on special curves and time-optimal control problems (1981) (0)

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