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Mathematical Proceedings of the Cambridge Philosophical Society, 1941
Suppose that n runs through all integral values, that (øn) is a system of normal orthogonal functions for the interval (−∞, ∞), and that ψn is the Fourier transform of øn. Then, by Parseval's theorem for Fourier transforms,and (ψn) is also a normal orthogonal system.
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Suppose that n runs through all integral values, that (øn) is a system of normal orthogonal functions for the interval (−∞, ∞), and that ψn is the Fourier transform of øn. Then, by Parseval's theorem for Fourier transforms,and (ψn) is also a normal orthogonal system.
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Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 2009
The transverse function approach, a control design method initially developed by the authors for nonlinear driftless systems, is based on a theorem that establishes the equivalence between the satisfaction of the Lie algebra rank condition (LARC) by a family of vector fields and the existence of functions “transverse” to these vector fields, defined on
Pascal Morin, Claude Samson
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The transverse function approach, a control design method initially developed by the authors for nonlinear driftless systems, is based on a theorem that establishes the equivalence between the satisfaction of the Lie algebra rank condition (LARC) by a family of vector fields and the existence of functions “transverse” to these vector fields, defined on
Pascal Morin, Claude Samson
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Orthogonal Polynomials and Special Functions: Recent Trends and Their Applications
exaly +2 more sourcesCharacterization of special classes of solutions for some functional equations on orthogonal vectors
Aequationes Mathematicae, 2000The author deals with two functional equations restricted to the orthogonal vectors, namely \[ g(x+y)g(x-y)=\bigl(g(x) \bigr)^2+ \bigl(g(y) \bigr)^2 \] (for all \(x,y\in X\) with \((x,y)=0)\) and \[ g(x+y)g(x-y)=\bigl( g(x) \bigr)^2 +\bigl(g(y) \bigr)^2-1, \] (for all \(x,y\in X\) with \((x,y)=0)\), where \(g:X\to \mathbb{R}\) and \(X\) is a real inner
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Some special functions in orthogonal fuzzy bipolar metric spaces and their fixed point applications
Numerical Methods for Partial Differential Equations, 2020AbstractIn this work, we synthesize orthogonal and bipolar metric issues and tried to deal with them in fuzzy metric spaces. We introduce a new concept of orthogonal fuzzy bipolar metric space and prove some fixed point theorems for some contractions in this space. Also, we provide some examples to illustrate the validity of the results obtained in the
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Computer Algebra Algorithms for Orthogonal Polynomials and Special Functions
2003In this minicourse I would like to present computer algebra algorithms for the work with orthogonal polynomials and special functions. This includes •the computation of power series representations of hypergeometric type functions, given by “expressions”, like arcsin(x)/x, • the computation of holonomic differential equations for functions ...
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Special functions of Weyl groups and their continuous and discrete orthogonality
2014Cette thèse s'intéresse à l'étude des propriétés et applications de quatre familles des fonctions spéciales associées aux groupes de Weyl et dénotées $C$, $S$, $S^s$ et $S^l$. Ces fonctions peuvent être vues comme des généralisations des polynômes de Tchebyshev.
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Unipotent class functions of split special orthogonal groups over finite fields
Communications in Algebra, 1984(1984). Unipotent class functions of split special orthogonal groups over finite fields. Communications in Algebra: Vol. 12, No. 5, pp. 517-615.
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The Space L 2. Orthogonal Systems, Fourier Series. Special Functions (Bessel Functions, Etc.)
1994In §13.14 the definition of functions square integrable on a set M has been given. In the present paragraph, this definition is specified for the case M a b], where [a b] is a bounded interval, and the so-called space L 2 a b) is introduced. At the end of the paragraph, the possibility is discussed how to define, in a similar way, the space L 2(Ω ...
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