Displaying similar documents to “Commuting linear operators and algebraic decompositions”

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 ℤ p the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, k ∞ a ℤ 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 ℤ 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...

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...

Non-compact perturbations of m -accretive operators in general Banach spaces

Mieczysław Cichoń (1992)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we deal with the Cauchy problem for differential inclusions governed by m -accretive operators in general Banach spaces. We are interested in finding the sufficient conditions for the existence of integral solutions of the problem x ' ( t ) ∈ - A x ( t ) + f ( t , x ( t ) ) , x ( 0 ) = x 0 , where A is an m -accretive operator, and f is a continuous, but non-compact perturbation, satisfying some additional conditions.