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resolvent integral

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  • Resolvent formalism — In mathematics, the resolvent formalism is a technique for applying concepts from complex analysis to the study of the spectrum of operators on Hilbert spaces and more general spaces.The resolvent captures the spectral properties of an operator… …   Wikipedia

  • Fredholm integral equation — In mathematics, the Fredholm integral equation is an integral equation whose solution gives rise to Fredholm theory, the study of Fredholm kernels and Fredholm operators. The integral equation was studied by Ivar Fredholm. Equation of the first… …   Wikipedia

  • Holomorphic functional calculus — In mathematics, holomorphic functional calculus is functional calculus with holomorphic functions. That is to say, given a holomorphic function fnof; of a complex argument z and an operator T , the aim is to construct an operator:f(T),which in a… …   Wikipedia

  • Fredholm theory — In mathematics, Fredholm theory is a theory of integral equations. In the narrowest sense, Fredholm theory concerns itself with the solution of the Fredholm integral equation. In a broader sense, the abstract structure of Fredholm s theory is… …   Wikipedia

  • Hilbert space — For the Hilbert space filling curve, see Hilbert curve. Hilbert spaces can be used to study the harmonics of vibrating strings. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It… …   Wikipedia

  • mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… …   Universalium

  • List of important publications in mathematics — One of the oldest surviving fragments of Euclid s Elements, found at Oxyrhynchus and dated to circa AD 100. The diagram accompanies Book II, Proposition 5.[1] This is a list of important publications in mathematics, organized by field. Some… …   Wikipedia

  • Sturm-Liouville theory — In mathematics and its applications, a classical Sturm Liouville equation, named after Jacques Charles François Sturm (1803 1855) and Joseph Liouville (1809 1882), is a real second order linear differential equation of the formwhere y is a… …   Wikipedia

  • Hilbert–Pólya conjecture — In mathematics, the Hilbert–Pólya conjecture is a possible approach to the Riemann hypothesis, by means of spectral theory.Initial hunchesDavid Hilbert and George Pólya speculated that real number values of t such that : frac12 + it is a zero of… …   Wikipedia

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  • Liouville-Neumann series — In mathematics, the Liouville Neumann series is an infinite series that corresponds to the resolvent formalism technique of solving the Fredholm integral equations in Fredholm theory.DefinitionThe Liouville Neumann series is defined as:phileft(x… …   Wikipedia

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