Jacques Hadamard

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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).

WORKS

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

REFERENCE

Lévy, P. “Zhak Adamar.” Uspekhi matematicheskikh nauk, 1964, vol. 19, no. 3 (117), pages 163–82. (Includes a list of Hadamard’s works.)
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As evidence for this phenomenon he recalled various experiences recounted by "giants" of science like Poincare, Hadamard (Hadamard 1945; Koestler 1989: 329), Dirac, Schrodinger.
Hadamard, Lectures on Cauchy's problem in linear partial differential equations, Dover Publications, New York, 1952.
In order to compress the transformed version of the matrix Y shown in equations (5) to (8), it has to be taken into account that due to the Hadamard division of the original matrices their elements are decimal numbers.
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indicates the Hadamard product, * indicates the complex conjugate, F and [F.
However, in the case g([tau]) = ln [tau] and a > 0, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the Hadamard fractional integral defined by
To confirm this, at least for large enough n, the prime number theorem, conjectured by Gauss and proved much later by Hadamard and Vallee-Poussin, can be brought into play.
Up to now, various signal denoising methods have been developed to analyze the vibration signals, such as finite impulse response filter (FIR) [8], time-frequency manifold [9], empirical mode decomposition (EMD) [10], curvelet transform [11], quantum Hadamard transformation [12], wavelet [13], and multiwavelets [14].
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In [4] Cerone and Dragomir have estimated differences of the Hadamard inequality as follows.
Moreover, since K [less than or equal to] 0 over all M the Hadamard theorem [1] implies that [exp.