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The LaplaceBeltrami operator on surfaces
, 2008
"... A solution for the mathematical problem of functional calculus with LaplaceBeltrami operator on surfaces with axial symmetry is found. A quantitative analysis of the spectrum is presented. 1 ..."
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A solution for the mathematical problem of functional calculus with LaplaceBeltrami operator on surfaces with axial symmetry is found. A quantitative analysis of the spectrum is presented. 1
4. The LaplaceBeltrami Operator
, 802
"... Definition A Cantor set is a compact, completely disconnected set without isolated points Theorem Any Cantor set is homeomorphic to {0, 1}N. L. B, “On the structure of perfect sets of points”, Proc. Akad. Amsterdam, 12, (1910), 785794. Hence without extra structure there is only one Cantor set. I.2 ..."
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Definition A Cantor set is a compact, completely disconnected set without isolated points Theorem Any Cantor set is homeomorphic to {0, 1}N. L. B, “On the structure of perfect sets of points”, Proc. Akad. Amsterdam, 12, (1910), 785794. Hence without extra structure there is only one Cantor set. I.2) Metrics Definition Let X be a set. A metric d on X is a map d: X × X 7 → R+ such that, for all x, y, z ∈ X (i) d(x, y) = 0 if and only if x = y, (ii) d(x, y) = d(y, x), (iii) d(x, y) ≤ d(x, z) + d(z, y). Definition A metric d on a set X is an ultrametric if it satisfies d(x, y) ≤ max{d(x, z), d(z, y)} for all family x, y, z of points of C. Given (C, d) a metric space, for > 0 let ∼ be the equivalence
Bohr Phenomena for LaplaceBeltrami Operators
"... We investigate a Bohr phenomenon on the spaces of solutions of weighted Laplace–Beltrami operators associated with the hyperbolic metric of the unit ball in CN. These solutions do not satisfy the usual maximum principle, and the spaces have natural bases none of whose members is a constant function. ..."
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Cited by 2 (1 self)
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We investigate a Bohr phenomenon on the spaces of solutions of weighted Laplace–Beltrami operators associated with the hyperbolic metric of the unit ball in CN. These solutions do not satisfy the usual maximum principle, and the spaces have natural bases none of whose members is a constant function
EIGENFUNCTIONS OF THE LAPLACEBELTRAMI OPERATOR ON HYPERBOLOIDS
, 803
"... Abstract. Eigenfunctions of the LaplaceBeltrami operator on a hyperboloid are studied in the spirit of the treatment of the spherical harmonics by Stein and Weiss. As a special case, a simple selfcontained proof of Laplace’s integral for a Legendre function is obtained. In [SW71, Chapter IV, Secti ..."
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Abstract. Eigenfunctions of the LaplaceBeltrami operator on a hyperboloid are studied in the spirit of the treatment of the spherical harmonics by Stein and Weiss. As a special case, a simple selfcontained proof of Laplace’s integral for a Legendre function is obtained. In [SW71, Chapter IV
On approximation of the Laplace–Beltrami operator and the Willmore energy of surfaces
, 2011
"... Discrete Laplace–Beltrami operators on polyhedral surfaces play an important role for various applications in geometry processing and related areas like physical simulation or computer graphics. While discretizations of the weak Laplace–Beltrami operator are wellstudied, less is known about the str ..."
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Cited by 6 (1 self)
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Discrete Laplace–Beltrami operators on polyhedral surfaces play an important role for various applications in geometry processing and related areas like physical simulation or computer graphics. While discretizations of the weak Laplace–Beltrami operator are wellstudied, less is known about
The conformally invariant LaplaceBeltrami operator and factor ordering
, 2004
"... In quantum mechanics the kinetic energy term for a single particle is usually written in the form of the LaplaceBeltrami operator. This operator is a factor ordering of the classical kinetic energy. We investigate other relatively simple factor orderings and show that the only other solution for a ..."
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Cited by 1 (0 self)
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In quantum mechanics the kinetic energy term for a single particle is usually written in the form of the LaplaceBeltrami operator. This operator is a factor ordering of the classical kinetic energy. We investigate other relatively simple factor orderings and show that the only other solution for a
AN APPLICATION OF SCATTERING THEORY TO THE SPECTRUM OF THE LAPLACEBELTRAMI OPERATOR
, 2003
"... Abstract. Applying a theorem due to Belopol’ski and Birman, we show that the LaplaceBeltrami operator on 1forms on R n endowed with an asymptotically Euclidean metric has absolutely continuous spectrum equal to [0, +∞). 1. ..."
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Abstract. Applying a theorem due to Belopol’ski and Birman, we show that the LaplaceBeltrami operator on 1forms on R n endowed with an asymptotically Euclidean metric has absolutely continuous spectrum equal to [0, +∞). 1.
Results 1  10
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93,197