Results 201 to 210 of about 1,880,861 (238)
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2007
Consider the two Hilbert spaces H − and T−. Let K +: H − → T- be a bounded operator. Consider a measure ρ on H -. Denote by ρK the image of the measure ρ under K +. This paper aims to study the measure ρK assuming ρ to be the spectral measure of a Jacobi field. We present a family of operators whose spectral measure equals ρK.
Yurij M. Berezansky, Artem D. Pulemyotov
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Consider the two Hilbert spaces H − and T−. Let K +: H − → T- be a bounded operator. Consider a measure ρ on H -. Denote by ρK the image of the measure ρ under K +. This paper aims to study the measure ρK assuming ρ to be the spectral measure of a Jacobi field. We present a family of operators whose spectral measure equals ρK.
Yurij M. Berezansky, Artem D. Pulemyotov
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Jacobi fields and geodesic spheres
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1979SynopsisThis is a contribution to the general problem of determining the extent to which the geometry of a riemannian manifold is determined by properties of its geodesic spheres. In particular we show that total umbilicity of geodesic spheres determines riemannian manifolds of constant sectional curvature; quasi-umbilicity of geodesic spheres ...
Vanhecke, Lieven, Willmore, T. J.
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JACOBI FIELDS IN GEODESIC SURFACE CONGRUENCES
International Journal of Geometric Methods in Modern Physics, 2010Using the Nambu–Goto string action in the space of the surfaces spanned by closed strings in a spacetime manifold, we investigated the geodesic surface equation in the space of surfaces joining two given strings and the geodesic surface deviation equation in geodesic surface congruence which yields a Jacobi field along a given geodesic surface, and ...
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Floquet exponents for Jacobi fields
Ergodic Theory and Dynamical Systems, 1991AbstractThis paper introduces a Riemannian invariant of a compact Riemannian manifold based on the spectral theory for the Jacobi field operator. It is the Floquet exponent for this operator, a purely dynamical quantity computable directly from the asymptotic behavior of Jacobi fields.
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Jacobi Fields, Conjugate Points
1992Let us go back to the action principle as realized by Jacobi, i.e., time is eliminated, so we are dealing with the space trajectory of a particle. In particular, we want to investigate the conditions under which a path is a minimum of the action and those under which it is merely an extremum.
Walter Dittrich, Martin Reuter
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Abelian fields generated by a Jacobi sum
Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 1996Let \(m\) be a natural number, \(K=\mathbb{Q} (\zeta_m)\) the \(m\)-th cyclotomic field, \(p\) a prime number \(p\nmid m\) and \(P\) a prime of \(K\) lying over \(p\). For every tuple \(\alpha\in (\mathbb{Z}/m \mathbb{Z})^{n+2}\) \((n\geq 0)\) \(J_\alpha(P)\) is an element of \(K\) and the question is to determine the field \(\mathbb{Q} (J_\alpha(P))\).
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2008
Consider the two Hilbert spaces H− and T−. Let K+ : H− → T− be a bounded operator. Consider a measure ρ on H−. Denote by ρK the image of the measure ρ under K+. This paper aims to study the measure ρK assuming ρ to be the spectral measure of a Jacobi field. We present a family of operators whose spectral measure equals ρK.
Berezansky, Yurij M., Pulemotov, Artem
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Consider the two Hilbert spaces H− and T−. Let K+ : H− → T− be a bounded operator. Consider a measure ρ on H−. Denote by ρK the image of the measure ρ under K+. This paper aims to study the measure ρK assuming ρ to be the spectral measure of a Jacobi field. We present a family of operators whose spectral measure equals ρK.
Berezansky, Yurij M., Pulemotov, Artem
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Jacobi fields on a Riemann manifold
Ukrainian Mathematical Journal, 2006Some properties of Jacobi fields on a manifold of nonpositive curvature are considered. As a result, we obtain relations for derivatives of one class of functions on the manifold.
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Jacobi fields for a nonholonomic distribution
Vestnik St. Petersburg University: Mathematics, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Quantum computational Jacobi fields
2010Summary: In the Riemannian geometry of quantum computation, the quantum evolution is described in terms of the special unitary group of n-qubit unitary operators with unit determinant. To elaborate on several aspects of the methodology, the Riemannian curvature, geodesic equation, Jacobi equation, and lifted Jacobi equation on the group manifold are ...
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