Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: In this article, the authors present results obtained by using another classical method, namely the representation of solutions of such equations by compact complex contour integrals (for the hypergeometric equation this method goes back to [8]).
Abstract: Let G be a noncompact connected real semisimple Lie group with finite centre. The asymptotic behaviour of Eisenstein integrals associated with a minimal parabolic subgroup of G has to a large extent been studied by HarishChandra (unpublished work, see [12] for an account, and later in a more general setting in [5-7]). Other references are [9 and 10]. Harish-Chandra's work depends heavily on a detailed study of systems of differential equations satisfied by these integrals. In [1] it is shown that these systems can be transformed into complex differential equations of the regular singular type; the asymptotic behaviour of their solutions is studied by essentially applying the classical Frobenius theory. In this announcement we present some results obtained by using another classical method, namely the representation of solutions of such equations by compact complex contour integrals (for the hypergeometric equation this method goes back to [8]). These integral representations can serve as the starting point for estimation by application of the method of steepest descent. This is closely connected with the use of the method of stationary phase in [2], where the asymptotic behaviour of Eisenstein integrals with respect to the spectral variable is studied. I would like to thank Professor J. J. Duistermaat for suggesting this problem and for the many stimulating discussions we had. Let G = KAN be an Iwasawa decomposition. Let
4 citations
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TL;DR: In this paper, exact efficient asymptotic stability criteria for two-parameter systems of two autonomous delay differential equations were established, and exact efficient stability criteria were established for twoparameter system with two differentiable differential equations.
Abstract: We establish exact efficient asymptotic stability criteria for two-parameter systems of two autonomous delay differential equations
4 citations
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4 citations
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TL;DR: In this article, the construction of uniform asymptotic expansions of parabolic cylinder functions based on integral representations and the theory of linear differential equations has been studied, and some previous errors in the literature are corrected.
Abstract: Methods are discussed for the construction of uniform asymptotic expansions of parabolic cylinder functions of large order, based on integral representations and the theory of linear differential equations. Some previous errors in the literature are corrected.
4 citations
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4 citations