A class of generalized uniform asymptotic expansions.
A formal series solution of the one-dimensional Schrödinger equation
A new Taylor type formula and extensions for asymptotically developable functions
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 extensions from any subpolysector; the Gevrey case is included.
A perturbation-based model for rectifier circuits.
A WKB analysis of the Alfvén spectrum of the linearized magnetohydrodynamics equations
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, where may have singularities in the domaind of definition. We study the case when is a half-plane and possesses high Fourier components, analyzing the changes brought about by the singularity . We show that absorptions of energy takes...
Absolutely convergent expansions associated with a boundary-value problem with the eigenvalue parameter contained in one boundary condition
Almost everywhere convergence of the inverse Jacobi transform and endpoint results for a disc multiplier
The maximal operator S⁎ for the spherical summation operator (or disc multiplier) associated with the Jacobi transform through the defining relation for a function f on ℝ is shown to be bounded from into for (4α + 4)/(2α + 3) < p ≤ 2. Moreover S⁎ is bounded from into . In particular converges almost everywhere towards f, for , whenever (4α + 4)/(2α + 3) < p ≤ 2.
An existence theorem for certain solutions of algebraic differential equations in sectors
An extension of the Newton-Puiseux polygon construction to give solutions of Pfaffian forms
We give a proof of the fact that any holomorphic Pfaffian form in two variables has a convergent integral curve. The proof gives an effective method to construct the solution, and we extend it to get a Gevrey type solution for a Gevrey form.
Analysis of singularities and of integrability of ODE's by algorithms of Power Geometry
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...
Analytical approximation to solutions of singularly perturbed boundary value problems.
Application of uniform asymptotics to the fifth Painlevé transcendent.
Approssimabilità degli zeri di una funzione mediante gli zeri di una sua espressione asintotica. Applicazione alle soluzioni delle equazioni differenziali lineari del secondo ordine
Asymptotic analyses of two fourth order linear differential equations
Asymptotic analysis by the saddle point method of the Anick-Mitra-Sondhi model.
Asymptotic Analysis of Delay Differential Equations.
Asymptotic analysis of the Askey-scheme I: from Krawtchouk to Charlier
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.
Asymptotic analysis of the Carrier-Pearson problem.
Asymptotic and oscillation properties of third order linear differential equations
Asymptotic behavior of non-linear differential equations via non-standard analysis. Part III. Boundedness and monotone behavior of the equation (a(t)φ(x)x')' + c(t)f(x) = q(t)