Displaying similar documents to “Stević-Sharma type operators on Fock spaces in several variables”

-regularity for the -equation with a support condition

Shaban Khidr, Osama Abdelkader (2017)

Czechoslovak Mathematical Journal

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Let be a -convex intersection, , , in a complex manifold of complex dimension , , and let be a holomorphic vector bundle of rank over . In this paper, -estimates, , for solutions to the -equation with small loss of smoothness are obtained for -valued -forms on when . In addition, we solve the -equation with a support condition in -spaces. More precisely, we prove that for a -closed form in , , , with compact support and for with there...

Linear maps preserving -unitary operators

Abdellatif Chahbi, Samir Kabbaj, Ahmed Charifi (2016)

Mathematica Bohemica

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Let be a complex Hilbert space, a positive operator with closed range in and the sub-algebra of of all -self-adjoint operators. Assume onto itself is a linear continuous map. This paper shows that if preserves -unitary operators such that then defined by is a homomorphism or an anti-homomorphism and for all , where and is the Moore-Penrose inverse of . A similar result is also true if preserves -quasi-unitary operators in both directions such that there...

Sum-product theorems and incidence geometry

Mei-Chu Chang, Jozsef Solymosi (2007)

Journal of the European Mathematical Society

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In this paper we prove the following theorems in incidence geometry. 1. There is such that for any , and , if there are many distinct lines between and for all , , then are collinear. If the number of the distinct lines is then the cross ratio of the four points is algebraic. 2. Given , there is such that for any noncollinear, and , if there are many distinct lines between and for all , , then for any , we have distinct lines between and . 3. Given...

Generalized versions of Ilmanen lemma: Insertion of or functions

Václav Kryštof (2018)

Commentationes Mathematicae Universitatis Carolinae

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We prove that for a normed linear space , if is continuous and semiconvex with modulus , is continuous and semiconcave with modulus and , then there exists such that . Using this result we prove a generalization of Ilmanen lemma (which deals with the case ) to the case of an arbitrary nontrivial modulus . This generalization (where a function is inserted) gives a positive answer to a problem formulated by A. Fathi and M. Zavidovique in 2010.

Involutivity degree of a distribution at superdensity points of its tangencies

Silvano Delladio (2021)

Archivum Mathematicum

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Let (with ) be vector fields of class in an open set , let be a -dimensional submanifold of and define where is the tangent space to at . Then we expect the following property, which is obvious in the special case when is an interior point (relative to ) of : If is a -density point (relative to ) of then all the iterated Lie brackets of order less or equal to belong to . Such a property has been proved in [9] for and its proof in the...

A Note on Transcendental Power Series Mapping the Set of Rational Numbers into Itself

Diego Marques, Elaine Silva (2017)

Communications in Mathematics

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In this note, we prove that there is no transcendental entire function such that and , for all sufficiently large , where .

Admissible spaces for a first order differential equation with delayed argument

Nina A. Chernyavskaya, Lela S. Dorel, Leonid A. Shuster (2019)

Czechoslovak Mathematical Journal

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We consider the equation where and () are positive continuous functions for all and . By a solution of the equation we mean any function , continuously differentiable everywhere in , which satisfies the equation for all . We show that under certain additional conditions on the functions and , the above equation has a unique solution , satisfying the inequality where the constant does not depend on the choice of .