Generalized function

In mathematics, generalized functions are objects extending the notion of functions. There is more than one recognized theory, for example the theory of distributions. Generalized functions are especially useful in making discontinuous functions more like smooth functions, and describing discrete physical phenomena such as point charges. They are applied extensively, especially in physics and engineering.

Comment
enIn mathematics, generalized functions are objects extending the notion of functions. There is more than one recognized theory, for example the theory of distributions. Generalized functions are especially useful in making discontinuous functions more like smooth functions, and describing discrete physical phenomena such as point charges. They are applied extensively, especially in physics and engineering.
Has abstract
enIn mathematics, generalized functions are objects extending the notion of functions. There is more than one recognized theory, for example the theory of distributions. Generalized functions are especially useful in making discontinuous functions more like smooth functions, and describing discrete physical phenomena such as point charges. They are applied extensively, especially in physics and engineering. A common feature of some of the approaches is that they build on operator aspects of everyday, numerical functions. The early history is connected with some ideas on operational calculus, and more contemporary developments in certain directions are closely related to ideas of Mikio Sato, on what he calls algebraic analysis. Important influences on the subject have been the technical requirements of theories of partial differential equations, and group representation theory.
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Generalized function
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enGeneralized function
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Adelic algebraic group
Algebra
Algebraic analysis
Almost everywhere
Analytic function
André Weil
Applied mathematics
Associative
Beppo-Levi space
Category:Generalized functions
Charge density
Colombeau algebra
Compact support
Convolution
De Rham cohomology
De Rham current
Differential algebra
Differential form
Dimensional regularization
Dirac delta function
Discontinuous function
Distribution (mathematics)
Divergent series
Dual space
Engineering
Explicit formula of an L-function
Factor space
Field of fractions
Filter base
Fourier series
Fourier transformation
Function (mathematics)
Functional analysis
Function domain
Function space
Generalized eigenfunction
Generalized number
Green's function
Group representation
Hagen Kleinert
Heuristic
Hyperfunction
I.M. Gel'fand
Idele group
Integrable function
Integral domain
James Lighthill
Jan Mikusinski
Kurt Friedrichs
Laplace transform
Laplacian of the indicator
Lars Hörmander
Laurent Schwartz
Lebesgue integral
Limit of a distribution
Linear
Linear functional
Locally compact group
Manifold
Mathematical analysis
Mathematical singularity
Mathematics
Measure (mathematics)
Mikio Sato
Mollifier
Moment (mathematics)
Non-linear
Non-standard analysis
Number theory
Oliver Heaviside
Operational calculus
Operator (mathematics)
Partial differential equation
Partial differential equation theory
Path integral formulation
Paul Dirac
Physics
Point charge
Pure mathematics
Quantum mechanics
Restriction (mathematics)
Riemann
Rigged Hilbert space
Salomon Bochner
Schrödinger
Schwartz–Bruhat function
Scientific formalism
Sergei Sobolev
Sheaf (mathematics)
Sheaf theory
Singular support
Smooth function
Stokes' theorem
Support (mathematics)
Tate's thesis
Test function
Topological vector space
Trigonometric series
Vector bundle
Wave front set
Wave propagation
Weak derivative
Weak solution
Yuri Vladimirovich Egorov
Zeta distribution (number theory)
SameAs
51Vax
Função generalizada
Generalized function
m.05d169
Q846537
دالة معممة
广义函数
超関数
Subject
Category:Generalized functions
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