orthogonal functions


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orthogonal functions

[ȯr′thäg·ən·əl ′fəŋk·shənz]
(mathematics)
Two real-valued functions are orthogonal if their inner product vanishes.
References in periodicals archive ?
Kozlov, On the complete systems of orthogonal functions [in Russian], Mat.
Paley, A remarkable set of orthogonal functions, Proc.
Continuous time dynamical systems; state estimation and optimal control with orthogonal functions.
Writing for control students and engineers, they examine such topics as orthogonal functions and their properties, linear optimal control systems incorporating observers, linear-quadratic-Gaussian control, the optimal control of time-delay systems, and the hierarchical control of linear systems.
After an introduction to signals and systems, including properties of the delta function and some classical orthogonal functions, the book provides examples and applications of numerous transforms.
Hardy, Notes on special systems of orthogonal functions, IV: The orthogonal functions of Whittaker's cardinal series, Proc.
DAVIS, An application of doubly orthogonal functions to a problem of approximation in two regions, Trans.
He starts with the basic principles of electromagnetic theory, then moves to analytical methods and orthogonal functions, Green's functions, computer integration and conformal mapping, Fourier transform methods, computational methods, method of finite differences, finite difference time domain analysis, and variational methods.
k](r))} is no longer a set of orthogonal functions.
For linear operators, as Radon transform, since no boundary conditions are needed, the set is unique and depends only on the chosen basis and the chosen integration domain The method can be extended to inner products with weights different than unity as well as to orthogonal functions in general.
In this way one obtains one or two sets of orthogonal functions, which are expressed in terms of a dual set of q-orthogonal polynomials (which corresponds to the indeterminate moment problem).
If an orthogonality measure [mu] is not extremal, then it is important to find a system of orthogonal functions {[f.

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