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.
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- 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.
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- 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
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- Category:Generalized functions
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- Generalized function?oldid=1120161970&ns=0
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