Théorie des distributions à valeurs vectorielles. II

Schwartz, Laurent

doi:10.5802/aif.77

Cited by 352 publications

(497 citation statements)

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“…Indeed, Hadamard regularization is a well-established procedure in order to give sense to infinite integrals. It is not to be found in the classical books on infinite calculus by Hardy or Knopp; it was L. Schwartz [15] who popularized it, rescuing Hadamard's original papers. Nowadays, Hadamard convergence is one of the cornerstones in the rigorous formulation of QFT through micro-localization, which on its turn is considered by specialists to be the most important step towards the understanding of linear PDEs since the invention of distributions (for a beautiful, updated treatment of Hadamard's regularization see [16]).…”

Section: How To Deal With the Infinitiesmentioning

confidence: 99%

On the issue of imposing boundary conditions on quantum fields

Elizalde

2003

J. Phys. A: Math. Gen.

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An interesting example of the deep interrelation between Physics and Mathematics is obtained when trying to impose mathematical boundary conditions on physical quantum fields. This procedure has recently been re-examined with care. Comments on that and previous analysis are here provided, together with considerations on the results of the purely mathematical zeta-function method, in an attempt at clarifying the issue. Hadamard regularization is invoked in order to fill the gap between the infinities appearing in the QFT renormalized results and the finite values obtained in the literature with other procedures.

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Section: How To Deal With the Infinitiesmentioning

confidence: 99%

On the issue of imposing boundary conditions on quantum fields

Elizalde

2003

J. Phys. A: Math. Gen.

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“…In the following, we will use the notation The distribution fiK is a measure if and only if pk(J~) > 0 for all / > 0, / G Cex,(S"-x), see [42]. Let g = R~xf.…”

Section: Characterizations and Inequalities Of Intersection Bodiesmentioning

confidence: 99%

Centered bodies and dual mixed volumes

Zhang¹

1994

Trans. Amer. Math. Soc.

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Abstract. We establish a number of characterizations and inequalities for intersection bodies, polar projection bodies and curvature images of projection bodies in R" by using dual mixed volumes. One of the inequalities is between the dual Quermassintegrals of centered bodies and the dual Quermassintegrals of their central (n -l)-slices. It implies Lutwak's affirmative answer to the Busemann-Petty problem when the body with the smaller sections is an intersection body. We introduce and study the intersection body of order i of a star body, which is dual to the projection body of order i of a convex body. We show that every sufficiently smooth centered body is a generalized intersection body. We discuss a type of selfadjoint elliptic differential operator associated with a convex body. These operators give the openness property of the class of curvature functions of convex bodies. They also give an existence theorem related to a well-known uniqueness theorem about deformations of convex hypersurfaces in global differential geometry.

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“…In addition we have H ⊂ S ⊂ S ′ ⊂ Λ ∞ , where S is the Schwartz space of rapidly decreasing test functions (ref [32]). …”

Section: Distributions Of Exponential Typementioning

confidence: 99%