Distribution (Functional)
A functional distribution, also called a Generalized Function, is a generalization of theconcept of a function. Functional distributions are defined as continuous linear Functionals over aSpace of infinitely differentiable functions such that all continuous functions have SchwarzianDerivatives which are themselves distributions. The most commonly encountered functionaldistribution is the Delta Function.
See also Delta Function, Generalized Function, Schwarzian Derivative
References
Friedlander, F. G. Introduction to the Theory of Distributions. Cambridge, England: Cambridge University Press, 1982. Gel'fand, I. M. and Shilov, G. E. Generalized Functions, Vol. 1: Properties and Operations. New York: Harcourt Brace, 1977. Gel'fand, I. M. and Shilov, G. E. Generalized Functions, Vol. 2: Spaces of Fundamental and Generalized Functions. New York: Harcourt Brace, 1977. Gel'fand, I. M. and Shilov, G. E. Generalized Functions, Vol. 3: Theory of Differential Equations. New York: Harcourt Brace, 1977. Gel'fand, I. M. and Vilenkin, N. Ya. Generalized Functions, Vol. 4: Applications of Harmonic Analysis. New York: Harcourt Brace, 1977. Gel'fand, I. M.; Graev, M. I.; and Vilenkin, N. Ya. Generalized Functions, Vol. 5: Integral Geometry and Representation Theory. New York: Harcourt Brace, 1977. Griffel, D. H. Applied Functional Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1984. Halperin, I. and Schwartz, L. Introduction to the Theory of Distributions, Based on the Lectures Given by Laurent Schwarz. Toronto, Canada: University of Toronto Press, 1952. Lighthill, M. J. Introduction to Fourier Analysis and Generalised Functions. Cambridge, England: Cambridge University Press, 1958. Richards, I. and Young, H. The Theory of Distributions: A Nontechnical Introduction. New York: Cambridge University Press, 1995. Rudin, W. Functional Analysis, 2nd ed. New York: McGraw-Hill, 1991. Strichartz, R. Fourier Transforms and Distribution Theory. Boca Raton, FL: CRC Press, 1993. Zemanian, A. H. Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, with Applications. New York: Dover, 1987.
Distribution Theory
- Cupola
- Cupolarotunda
- Curl
- Curlicue Fractal
- Curl Theorem
- Current
- Curtate Cycloid
- Curtate Cycloid Evolute
- Curvature
- Curvature Center
- Curvature Scalar
- Curvature Vector
- Curve
- Curve of Constant Breadth
- Curve of Constant Precession
- Curve of Constant Slope
- Curve of Constant Width
- Curvilinear Coordinates
- Cushion
- Cusp
- Cusp Catastrophe
- Cusp Form
- Cusp Map
- Cusp Point
- Cutting