Displaying similar documents to “Equivalent norms in some spaces of analytic functions and the uncertainty principle”

Oblique derivative problem for elliptic equations in non-divergence form with V M O coefficients

Giuseppe di Fazio, Dian K. Palagachev (1996)

Commentationes Mathematicae Universitatis Carolinae

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A priori estimates and strong solvability results in Sobolev space W 2 , p ( Ω ) , 1 < p < are proved for the regular oblique derivative problem i , j = 1 n a i j ( x ) 2 u x i x j = f ( x ) a.e. Ω u + σ ( x ) u = ϕ ( x ) on Ω when the principal coefficients a i j are V M O L functions.

Guidance properties of a cylindrical defocusing waveguide

Oldřich John, Charles A. Stuart (1994)

Commentationes Mathematicae Universitatis Carolinae

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We discuss the propagation of electromagnetic waves of a special form through an inhomogeneous isotropic medium which has a cylindrical symmetry and a nonlinear dielectric response. For the case where this response is of self-focusing type the problem is treated in [1]. Here we continue this study by dealing with a defocusing dielectric response. This tends to inhibit the guidance properties of the medium and so guidance can only be expected provided that the cylindrical stratification...

On the vanishing of Iwasawa invariants of absolutely abelian p-extensions

Gen Yamamoto (2000)

Acta Arithmetica

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1. Introduction. Let p be a prime number and p the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, k a p -extension of k, k n the nth layer of k / k , and A n the p-Sylow subgroup of the ideal class group of k n . Iwasawa proved the following well-known theorem about the order A n of A n : Theorem A (Iwasawa). Let k / k be a p -extension and A n the p-Sylow subgroup of the ideal class group of k n , where k n is the n th layer of k / k . Then there exist integers λ = λ ( k / k ) 0 , μ = μ ( k / k ) 0 , ν = ν ( k / k ) , and n₀ ≥ 0...

Existence of solutions of degenerated unilateral problems with L 1 data

Lahsen Aharouch, Youssef Akdim (2004)

Annales mathématiques Blaise Pascal

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In this paper, we shall be concerned with the existence result of the Degenerated unilateral problem associated to the equation of the type A u + g ( x , u , u ) = f - div F , where A is a Leray-Lions operator and g is a Carathéodory function having natural growth with respect to | u | and satisfying the sign condition. The second term is such that, f L 1 ( Ω ) and F Π i = 1 N L p ( Ω , w i 1 - p ) .

Kneser’s theorem for upper Banach density

Prerna Bihani, Renling Jin (2006)

Journal de Théorie des Nombres de Bordeaux

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Suppose A is a set of non-negative integers with upper Banach density α (see definition below) and the upper Banach density of A + A is less than 2 α . We characterize the structure of A + A by showing the following: There is a positive integer g and a set W , which is the union of 2 α g - 1 arithmetic sequences [We call a set of the form a + d an arithmetic sequence of difference d and call a set of the form { a , a + d , a + 2 d , ... , a + k d } an arithmetic progression of difference d . So an arithmetic progression is finite and an arithmetic...