De rham regularization operators in orlicz spaces of differential forms on Riemannian manifolds

Yaroslav Anatol evich Kopylov; Roman Anatol evich Panenko

De rham regularization operators in orlicz spaces of differential forms on Riemannian manifolds

Yaroslav Anatol evich Kopylov, Roman Anatol evich Panenko

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In his classical monograph Variétés Différentiables (Paris: Hermann, 1955), G. de Rham introduced smoothing operators on currents on a differentiable manifold. We study some properties of the restrictions of these operators to Orlicz spaces of differential forms on a Riemannian manifold. In particular, we prove that if an N-function Φ is Δ₂-regular then the L_Φ-cohomology of a Riemannian manifold can be calculated with the use of smooth L^Φ-forms.

Original language	English
Pages (from-to)	361-371
Number of pages	11
Journal	Siberian Electronic Mathematical Reports
Volume	12
State	Published - 1 Jan 2015
Externally published	Yes

Keywords

De Rham regularization operator
Differential form
L-cohomology
Operator of exterior derivation
Orlicz space
Riemannian manifold

ASJC Scopus subject areas

General Mathematics

Cite this

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title = "De rham regularization operators in orlicz spaces of differential forms on Riemannian manifolds",

abstract = "In his classical monograph Vari{\'e}t{\'e}s Diff{\'e}rentiables (Paris: Hermann, 1955), G. de Rham introduced smoothing operators on currents on a differentiable manifold. We study some properties of the restrictions of these operators to Orlicz spaces of differential forms on a Riemannian manifold. In particular, we prove that if an N-function Φ is Δ2-regular then the LΦ-cohomology of a Riemannian manifold can be calculated with the use of smooth LΦ-forms.",

keywords = "De Rham regularization operator, Differential form, L-cohomology, Operator of exterior derivation, Orlicz space, Riemannian manifold",

author = "Kopylov, {Yaroslav Anatol evich} and Panenko, {Roman Anatol evich}",

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year = "2015",

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AU - Kopylov, Yaroslav Anatol evich

AU - Panenko, Roman Anatol evich

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N2 - In his classical monograph Variétés Différentiables (Paris: Hermann, 1955), G. de Rham introduced smoothing operators on currents on a differentiable manifold. We study some properties of the restrictions of these operators to Orlicz spaces of differential forms on a Riemannian manifold. In particular, we prove that if an N-function Φ is Δ2-regular then the LΦ-cohomology of a Riemannian manifold can be calculated with the use of smooth LΦ-forms.

AB - In his classical monograph Variétés Différentiables (Paris: Hermann, 1955), G. de Rham introduced smoothing operators on currents on a differentiable manifold. We study some properties of the restrictions of these operators to Orlicz spaces of differential forms on a Riemannian manifold. In particular, we prove that if an N-function Φ is Δ2-regular then the LΦ-cohomology of a Riemannian manifold can be calculated with the use of smooth LΦ-forms.

KW - De Rham regularization operator

KW - Differential form

KW - L-cohomology

KW - Operator of exterior derivation

KW - Orlicz space

KW - Riemannian manifold

UR - http://www.scopus.com/inward/record.url?scp=85007453866&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85007453866

SN - 1813-3304

VL - 12

SP - 361

EP - 371

JO - Siberian Electronic Mathematical Reports

JF - Siberian Electronic Mathematical Reports

ER -

De rham regularization operators in orlicz spaces of differential forms on Riemannian manifolds

Abstract

Keywords

ASJC Scopus subject areas

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