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Probabilistic Spherical MarcinkiewiczZygmund Inequalities
"... Recently, norm equivalences between spherical polynomials and their sample values at scattered sites have been proved. These socalled MarcinkiewiczZygmund inequalities involve a parameter that characterizes the density of the sampling set and they are applicable to all polynomials whose degree doe ..."
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Cited by 1 (0 self)
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Recently, norm equivalences between spherical polynomials and their sample values at scattered sites have been proved. These socalled MarcinkiewiczZygmund inequalities involve a parameter that characterizes the density of the sampling set and they are applicable to all polynomials whose degree
MarcinkiewiczZygmund inequalities
 J. Approx. Theory
, 2007
"... ABSTRACT. We study a generalization of the classical MarcinkiewiczZygmund inequalities. We relate this problem to the sampling sequences in the PaleyWiener space and by using this analogy we give sharp necessary and sufficient computable conditions for a family of points to satisfy the Marcinkiewi ..."
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Cited by 6 (1 self)
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ABSTRACT. We study a generalization of the classical MarcinkiewiczZygmund inequalities. We relate this problem to the sampling sequences in the PaleyWiener space and by using this analogy we give sharp necessary and sufficient computable conditions for a family of points to satisfy
Spherical MarcinkiewiczZygmund inequalities and positive quadrature
 Math. Comp
, 2002
"... Abstract. Geodetic and meteorological data, collected via satellites for example, are genuinely scattered and not confined to any special set of points. Even so, known quadrature formulas used in numerically computing integrals involving such data have had restrictions either on the sites (points) u ..."
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Cited by 63 (17 self)
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require only a number of sites comparable to the dimension of the space. As a part of the proof, we derive L 1MarcinkiewiczZygmund inequalities for such sites. 1.
MARCINKIEWICZZYGMUND INEQUALITIES AND INTERPOLATION BY SPHERICAL HARMONICS.
, 2006
"... ABSTRACT. We find necessary density conditions for MarcinkiewiczZygmund inequalities and interpolation for spaces of spherical harmonics in S d with respect to the L p norm. Moreover, we prove that there are no complete interpolation families for p ̸ = 2. 1. ..."
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ABSTRACT. We find necessary density conditions for MarcinkiewiczZygmund inequalities and interpolation for spaces of spherical harmonics in S d with respect to the L p norm. Moreover, we prove that there are no complete interpolation families for p ̸ = 2. 1.
Probabilistic MarcinkiewiczZygmund inequalities on the rotation group
, 2009
"... on the rotation group ..."
Ricci Flow with Surgery on ThreeManifolds
"... This is a technical paper, which is a continuation of [I]. Here we verify most of the assertions, made in [I, §13]; the exceptions are (1) the statement that a 3manifold which collapses with local lower bound for sectional curvature is a graph manifold this is deferred to a separate paper, as the ..."
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Cited by 454 (2 self)
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This is a technical paper, which is a continuation of [I]. Here we verify most of the assertions, made in [I, §13]; the exceptions are (1) the statement that a 3manifold which collapses with local lower bound for sectional curvature is a graph manifold this is deferred to a separate paper
Discrete DifferentialGeometry Operators for Triangulated 2Manifolds
, 2002
"... This paper provides a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging Vorono ..."
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Cited by 453 (17 self)
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This paper provides a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging Voronoi cells and the mixed FiniteElement/FiniteVolume method, and compare them to existing formulations. Building upon previous work in discrete geometry, these new operators are closely related to the continuous case, guaranteeing an appropriate extension from the continuous to the discrete setting: they respect most intrinsic properties of the continuous differential operators.
Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering
 Advances in Neural Information Processing Systems 14
, 2001
"... Drawing on the correspondence between the graph Laplacian, the LaplaceBeltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in a higher ..."
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Cited by 664 (8 self)
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Drawing on the correspondence between the graph Laplacian, the LaplaceBeltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in a
Superconformal field theory on threebranes at a CalabiYau singularity
 Nucl. Phys. B
, 1998
"... Just as parallel threebranes on a smooth manifold are related to string theory on AdS5 × S 5, parallel threebranes near a conical singularity are related to string theory on AdS5 × X5, for a suitable X5. For the example of the conifold singularity, for which X5 = (SU(2) × SU(2))/U(1), we argue that ..."
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Cited by 690 (37 self)
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Just as parallel threebranes on a smooth manifold are related to string theory on AdS5 × S 5, parallel threebranes near a conical singularity are related to string theory on AdS5 × X5, for a suitable X5. For the example of the conifold singularity, for which X5 = (SU(2) × SU(2))/U(1), we argue
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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’ of holomorphic curves of higher genus curves in Calabi–Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the corresponding N = 2
Results 1  10
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