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22 relations: Analytic function, Cauchy–Riemann equations, Complex number, Distribution (mathematics), Dominated convergence theorem, Entire function, Exponential type, Fourier transform, Generalized function, H square, Hardy space, Laplace transform, Laurent Schwartz, Lp space, Mathematics, McGraw-Hill Education, Norbert Wiener, Plancherel theorem, Raymond Paley, Square-integrable function, Support (mathematics), Upper half-plane.
Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series.
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Cauchy–Riemann equations
In the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which, together with certain continuity and differentiability criteria, form a necessary and sufficient condition for a complex function to be complex differentiable, that is, holomorphic.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Distribution (mathematics)
Distributions (or generalized functions) are objects that generalize the classical notion of functions in mathematical analysis.
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Dominated convergence theorem
In measure theory, Lebesgue's dominated convergence theorem provides sufficient conditions under which almost everywhere convergence of a sequence of functions implies convergence in the L1 norm.
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Entire function
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic at all finite points over the whole complex plane.
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Exponential type
In complex analysis, a branch of mathematics, a holomorphic function is said to be of exponential type C if its growth is bounded by the exponential function eC|z| for some real-valued constant C as |z| → ∞.
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Fourier transform
The Fourier transform (FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes.
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Generalized function
In mathematics, generalized functions, or distributions, are objects extending the notion of functions.
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H square
In mathematics and control theory, H2, or H-square is a Hardy space with square norm.
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Hardy space
In complex analysis, the Hardy spaces (or Hardy classes) Hp are certain spaces of holomorphic functions on the unit disk or upper half plane.
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Laplace transform
In mathematics, the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.
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Laurent Schwartz
Laurent-Moïse Schwartz (5 March 1915 – 4 July 2002) was a French mathematician.
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Lp space
In mathematics, the Lp spaces are function spaces defined using a natural generalization of the ''p''-norm for finite-dimensional vector spaces.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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McGraw-Hill Education
McGraw-Hill Education (MHE) is a learning science company and one of the "big three" educational publishers that provides customized educational content, software, and services for pre-K through postgraduate education.
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Norbert Wiener
Norbert Wiener (November 26, 1894 – March 18, 1964) was an American mathematician and philosopher.
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Plancherel theorem
In mathematics, the Plancherel theorem is a result in harmonic analysis, proven by Michel Plancherel in 1910.
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Raymond Paley
Raymond Edward Alan Christopher Paley (7 January 1907 – 7 April 1933) was an English mathematician.
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Square-integrable function
In mathematics, a square-integrable function, also called a quadratically integrable function, is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite.
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Support (mathematics)
In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero.
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Upper half-plane
In mathematics, the upper half-plane H is the set of complex numbers with positive imaginary part: The term arises from a common visualization of the complex number x + iy as the point (x,y) in the plane endowed with Cartesian coordinates.
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Paley-Weiner theorem, Paley-Wiener criterion, Paley-Wiener theorem, Payley-Wiener theorem.
References
[1] https://en.wikipedia.org/wiki/Paley–Wiener_theorem
