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A new Taylor type formula and C ∞ extensions for asymptotically developable functions

M. Zurro (1997)

Studia Mathematica

The paper studies the relation between asymptotically developable functions in several complex variables and their extensions as functions of real variables. A new Taylor type formula with integral remainder in several variables is an essential tool. We prove that strongly asymptotically developable functions defined on polysectors have C ∞ extensions from any subpolysector; the Gevrey case is included.

A WKB analysis of the Alfvén spectrum of the linearized magnetohydrodynamics equations

Manuel Núñez, Jesús Rojo (1993)

Applications of Mathematics

Small perturbations of an equilibrium plasma satisfy the linearized magnetohydrodynamics equations. These form a mixed elliptic-hyperbolic system that in a straight-field geometry and for a fixed time frequency may be reduced to a single scalar equation div A 1 Δ u + A 2 u = 0 , where A 1 may have singularities in the domaind U of definition. We study the case when U is a half-plane and u possesses high Fourier components, analyzing the changes brought about by the singularity A 1 = ∞ . We show that absorptions of energy takes...

Almost everywhere convergence of the inverse Jacobi transform and endpoint results for a disc multiplier

Troels Roussau Johansen (2011)

Studia Mathematica

The maximal operator S⁎ for the spherical summation operator (or disc multiplier) S R associated with the Jacobi transform through the defining relation S R f ^ ( λ ) = 1 | λ | ≤ R f ̂ ( t ) for a function f on ℝ is shown to be bounded from L p ( ℝ ₊ , d μ ) into L p ( ℝ , d μ ) + L ² ( ℝ , d μ ) for (4α + 4)/(2α + 3) < p ≤ 2. Moreover S⁎ is bounded from L p ₀ , 1 ( ℝ ₊ , d μ ) into L p ₀ , ∞ ( ℝ , d μ ) + L ² ( ℝ , d μ ) . In particular S R f ( t ) R > 0 converges almost everywhere towards f, for f ∈ L p ( ℝ ₊ , d μ ) , whenever (4α + 4)/(2α + 3) < p ≤ 2.

Analysis of singularities and of integrability of ODE's by algorithms of Power Geometry

Alexander D. Bruno (2011)

Banach Center Publications

Here we present basic ideas and algorithms of Power Geometry and give a survey of some of its applications. In Section 2, we consider one generic ordinary differential equation and demonstrate how to find asymptotic forms and asymptotic expansions of its solutions. In Section 3, we demonstrate how to find expansions of solutions to Painlevé equations by this method, and we analyze singularities of plane oscillations of a satellite on an elliptic orbit. In Section 4, we consider the problem of local...

Asymptotic analysis of the Askey-scheme I: from Krawtchouk to Charlier

Diego Dominici (2007)

Open Mathematics

We analyze the Charlier polynomials C n(χ) and their zeros asymptotically as n → ∞. We obtain asymptotic approximations, using the limit relation between the Krawtchouk and Charlier polynomials, involving some special functions. We give numerical examples showing the accuracy of our formulas.

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