Jacques Hadamard

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The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Hadamard, Jacques


Born Dec. 8, 1865, in Versailles; died Oct. 17, 1963, in Paris. French mathematician. Professor at the Collège de France, 1897–1935, Université de Paris (the Sorbonne), 1900–1912, Ecole Polytechnique from 1912; foreign member of the USSR Academy of Sciences from 1929.

Hadamard is known for his research in various branches of mathematics. In the theory of numbers he demonstrated, in 1896, P. L. Chebyshev’s proposed asymptotic law of the distribution of prime numbers. He originated a significant part of the modern theory of entire analytic functions and obtained substantial results in the theory of differential equations. His ideas were highly influential in the founding of functional analysis. In mechanics Hadamard’s concerns included problems of stability and the study of the properties of mechanical system trajectories close to the equilibrium position. He was also interested in school teaching and prepared a geometry textbook (in Russian translation, Elementarnaia Geometryiia, part 1, Moscow, 1948; part 2, 1938).


Lectures on Cauchy’s Problem. New York, 1923.
Cours d’analyse,vols. 1–2. Paris, 1927–30.
Selecta: Jubilé scientifique. Paris, 1935.


Lévy, P. “Zhak Adamar.” Uspekhi matematicheskikh nauk, 1964, vol. 19, no. 3 (117), pages 163–82. (Includes a list of Hadamard’s works.)
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
[13] applied the Hadamard energy for residual information measurement to determine the quantization parameter (QP) value for better coding efficiency.
Wang and Feckan extend classical Hermite-Hadamard type inequalities to the fractional case by establishing fractional identities, and discuss Riemann-Liouville and Hadamard integrals, respectively, by various convex functions.
where the integral on the right-hand side is defined as the finite part in the Hadamard sense.
The boundary variation method that we study is a classical idea well known and used before by Hadamard [3] in 1907 and many others as [4-12].
Another kind of fractional derivative is Hadamard type which was introduced in 1892 [11].
A well-posed inverse problem in the sense of Hadamard means that a solution for the inverse problem exists and that the solution is unique and continuous [9].
The convolution (or Hadamard product) of two series f(z) = [[summation].sup.[infinity].sub.n=0] [a.sub.n][z.sup.n] and g(z) = [[summation].sup.[infinity].sub.n=0][b.sub.n][z.sup.n] is defined as the power series:
Fitzpatrick, "The Hadamard inequalities for s-convex functions in the second sense," Demonstratio Mathematica, vol.
(vi) weak solutions for partial random Hadamard fractional integral equations with multiple delays,
So, the sequences that are derived by Walsh Hadamard matrix play an important role in CDM-based communication technology.
If all of the eigenvalues of the Hadamard product [A.sub.d] [??] E are located at the left-hand plane, then the S-system in (1) is stable, wherein the steady state parameter E is the outer product of the equilibrium flux vector [[bar.V].sup.+] and equilibrium state inverse vector [[??].sub.d]; i.e., E = [[bar.V].sup.+] [cross product] [[??].sub.d] where the vector [[??].sub.d] = [1 / [[bar.x].sub.1]] with i = 1, ..., n, and [[bar.x].sub.i]] denotes the dependent variable [x.sub.i] in equilibrium.