Results 31 to 40 of about 51,079 (125)
Non linear eigenvalue problems [PDF]
, 2004 In this paper we consider generalized eigenvalue problems for a family of operators with a polynomial dependence on a complex parameter. This problem is equivalent to a genuine non self-adjoint operator.
Robert, Didier
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Sum of squares manifolds: The expressibility of the Laplace-Beltrami operator on pseudo-Riemannian manifolds as a sum of squares of vector fields [PDF]
Transactions of the American Mathematical Society, 1998 The paper is devoted to a detailed study of the conditions under which the standard Laplace-Beltrami operator on pseudo-Riemannian manifolds could be expressed, either locally or globally, as the sum of squares of vector fields. After a careful explanation of the problem in the introduction, the ultimate general results for both local and global ...
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Solutions to Yang-Mills equations [PDF]
, 2010 This article gives explicit solutions to the Yang-Mills equations. The solutions have positive energy that can be made arbitrarily small by selection of a parameter showing that Yang-Mills field theories do not have a mass gap.Comment: minor corrections ...
Jormakka, Jorma
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Chapter 12 Hardy and Rellich Inequalities for Sums of Squares of Vector Fields [PDF]
, 2019 In this chapter, we demonstrate how some ideas originating in the analysis on groups can be applied in related settings without the group structure. In particular, in Chapter 7 we showed a number of Hardy and Rellich inequalities with weights expressed in terms of the so-called \(\mathcal{L}\)-gauge.
Michael Ruzhansky, Durvudkhan Suragan
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Universal quadratic forms, small norms and traces in families of number fields
, 2020 We obtain good estimates on the ranks of universal quadratic forms over Shanks' family of the simplest cubic fields and several other families of totally real number fields. As the main tool we characterize all the indecomposable integers in these fields
Kala, Vítězslav, Tinková, Magdaléna
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Fundamental solutions and geometry of the sum of squares of vector fields
Inventiones Mathematicae, 1984 Let \(X_ 1,...,X_ m\) be smooth vector fields on a smooth compact manifold M, endowed with a smooth positive measure \(\mu\). It is assumed that taking a sufficient number of commutators of \(X_ 1,...,X_ m\) they span the tangent of M at every point (Hörmander's condition). Then the operators like \(L=\sum^{m}_{j=1}X^ 2_ j+\sum^{m}_{i,j=1}f_{ij}[[ X_ i,
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A remark on sums of squares of complex vector fields
, 2005 This note is a comment on a recent paper by J. J. Kohn. We give an example of a second order partial differential operator, expressed as a sum of squares of complex vector fields satisfying the bracket condition, that is not hypoelliptic.
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Constructions of Mutually Unbiased Bases
, 2003 Two orthonormal bases B and B' of a d-dimensional complex inner-product space are called mutually unbiased if and only if ||^2=1/d holds for all b in B and b' in B'. The size of any set containing (pairwise) mutually unbiased bases of C^d cannot exceed d+
Klappenecker, Andreas, Roetteler, Martin
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Global Analytic Hypoellipticity for a Class of Quasilinear Sums of Squares of Vector Fields
, 2003 A global real analytic regularity theorem for a quasilinear sum of squares of vector fields of Hormander rank 2 is given. A related local result for a special case was proved recently by the second author and L. Zanghirati in a paper titled "Local Real Analyticity of Solutions for sums of squares of non-linear vector fields".
Derridj, Makhlouf, Tartakoff, David S.
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Mathematische Zeitschrift, 1992 We study the equations \[ \begin{aligned} \left( L - {\partial \over \partial t} \right) u(x,t) & = 0 \quad \text{ and }\tag{1.1} \\ Lu(x) & = 0 \tag{1.2}\end{aligned} \] associated to the operator \(L = \sum_ i X^ 2_ i - X_ 0\) on a compact manifold \(M\) with a positive measure \(\mu\), where \(X_ 1, X_ 2, \dots, X_ m\) are smooth vector fields on ...
Yau, Shing-Tung, Cao, Huai-Dong
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