Results 211 to 220 of about 6,332 (238)
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Ukrainian Mathematical Journal, 2005
We construct new examples of operators of generalized translation and convolutions in eigenfunctions of certain self-adjoint differential operators.
A. V. Kosyak, L. P. Nizhnik
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We construct new examples of operators of generalized translation and convolutions in eigenfunctions of certain self-adjoint differential operators.
A. V. Kosyak, L. P. Nizhnik
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Elements of Lie Theory for Generalized Translation Operators
1998As in the case of topological groups, there are two approaches to the investigation of generalized translation operators—global and infinitesimal. The first one includes the theory of representations, harmonic analysis, the theory of almost periodic functions, etc.
Yu. M. Berezansky, A. A. Kalyuzhnyi
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Infinite-dimensional non-gaussian analysis and generalized translation operators
Functional Analysis and Its Applications, 1996The author considers a family \(T= \{T_x\}_{x\in Q}\) of ``generalized translation operators'' on \(C(Q)\), \(Q\) being a separable complete metric space, and defines characters for such a family. Then he constructs non-Gaussian analogues of the Fock spaces for measures on \(Q\) and gives examples.
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Ukrainian Mathematical Journal, 1999
Summary: Pseudodifferential equations of the form \(v(D_{\chi})y=f,\) where \(v\) is a function holomorphic at zero and \(D_{\chi}\) is a pseudodifferential operator, are studied on spaces of test functions of non-Gaussian infinite-dimensional analysis. The results obtained are applied to construct a generalized translation operator \(T_{y}^{\chi}=\chi(
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Summary: Pseudodifferential equations of the form \(v(D_{\chi})y=f,\) where \(v\) is a function holomorphic at zero and \(D_{\chi}\) is a pseudodifferential operator, are studied on spaces of test functions of non-Gaussian infinite-dimensional analysis. The results obtained are applied to construct a generalized translation operator \(T_{y}^{\chi}=\chi(
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Journal of Mathematical Physics, 1973
The A and M transformation for finding an integral equation for the kernel of a generalized translation operator is adapted to the s-wave regular solution. Its extension to higher l-values is then considered for Jost solutions. The integral equations for the G.T.O. kernels are similar to the s wave one, with the difference that the Riemann function for
Coz, Marcel, Coudray, Christiane
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The A and M transformation for finding an integral equation for the kernel of a generalized translation operator is adapted to the s-wave regular solution. Its extension to higher l-values is then considered for Jost solutions. The integral equations for the G.T.O. kernels are similar to the s wave one, with the difference that the Riemann function for
Coz, Marcel, Coudray, Christiane
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Generalized translations associated with an unbounded self-adjoint operator
Mathematical Proceedings of the Cambridge Philosophical Society, 1986Delsarte [2], Povzner [9], Levitan [8], Leblanc [7], Dunford and Schwartz [3] (p. 1626) and Hutson and Pym [5] have discussed generalized translation operators (GTO) ‘associating with a differential operator’. The latter authors have also considered the topic in an abstract setting-the GTO ‘associates’ with a compact operator in a normed space. GTO are
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Infinite-dimensional analysis related to generalized translation operators
Ukrainian Mathematical Journal, 1997Let \(Q\) be a separable metric complete space with a Borel probability measure \(\rho\). The author treats here generalized translation operators, i.e. a family \(\{T_x\}\) of linear operators possessing the properties: \(\forall f\in C(Q)\), \(T_xf(y)= T_yf(x)\), \(x,y\in Q\), \(T_e= \text{id}.\), locality, and continuity. Character \(\chi(x,\lambda)\
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Doklady Mathematics, 2008
The paper investigates the \(C^{\ast}\)-algebra generated by integral operators on \(L_{2}({\mathbb R}^{n})\) with kernel homogeneous of degree \((-n)\) and invariant under the rotation group in \({\mathbb R}^{n}\), and by multiplicative translation operators (operators on the form \(f(x)\rightarrow \delta^{-n/2}f(x/\delta)\), \(\delta>0\)). The author
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The paper investigates the \(C^{\ast}\)-algebra generated by integral operators on \(L_{2}({\mathbb R}^{n})\) with kernel homogeneous of degree \((-n)\) and invariant under the rotation group in \({\mathbb R}^{n}\), and by multiplicative translation operators (operators on the form \(f(x)\rightarrow \delta^{-n/2}f(x/\delta)\), \(\delta>0\)). The author
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Generalized Translations Associated with a Differential Operator
Proceedings of the London Mathematical Society, 1972Hutson, V., Pym, J. S.
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