On the summability and convergence of formal solutions of linear \(q\)-difference-differential equations with constant coefficients. (English) Zbl 1541.35128
Reviewer: Pascal Remy (Carrières-sur-Seine)
Found 45 Documents (Results 1–45)
Asymptotic existence theorem for formal solutions with singularities of nonlinear partial differential equations via multisummability. (English) Zbl 1522.35148
Multisummability of formal solutions for a family of generalized singularly perturbed moment differential equations. (English) Zbl 1511.34088
Multi-resurgence and connection-to-Stokes formulæ for some linear meromorphic differential systems. (English) Zbl 1378.34098
Reviewer: Vladimir P. Kostov (Nice)
Analytic and summable solutions of inhomogeneous moment partial differential equations. (English) Zbl 1400.35067
Reviewer: Pascal Remy (Carrières-sur-Seine)
Resurgence and highest level’s connection-to-Stokes formulæ for some linear meromorphic differential systems. (English. French summary) Zbl 1384.34092
Reviewer: Vladimir P. Kostov (Nice)
Divergent series, summability and resurgence II. Simple and multiple summability. (English) Zbl 1348.34002
Lecture Notes in Mathematics 2154. Cham: Springer (ISBN 978-3-319-29074-4/pbk; 978-3-319-29075-1/ebook). xxiii, 272 p. (2016).
Reviewer: Vladimir P. Kostov (Nice)
On the multisummability of WKB solutions of certain singularly perturbed linear ordinary differential equations. (English) Zbl 1325.34105
Summability of formal solutions of linear partial differential equations with divergent initial data. (English) Zbl 1306.35007
Corrigendum to: “On the multisummability of divergent solutions of linear partial differential equations with constant coefficients”. (English) Zbl 1280.35025
Analytic solutions of moment partial differential equations with constant coefficients. (English) Zbl 1282.35129
Reviewer: Yoshitsugu Takei (Kyoto)
Multisummability and ordinary meromorphic differential equations. (English) Zbl 1262.34001
Balser, Werner (ed.) et al., Formal and analytic solutions of differential and difference equations. Proceedings of the conference, Bȩdlewo, Poland, August 8–13, 2011. Warszawa: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-16-4/pbk). Banach Center Publications 97, 29-38 (2012).
On the multisummability of divergent solutions of linear partial differential equations with constant coefficients. (English) Zbl 1195.35095
J. Differ. Equations 249, No. 3, 551-570 (2010); corrigendum ibid. 255, No. 8, 2400-2401 (2013).
Reviewer: Igor Andrianov (Köln)
Multisummability of formal power series solutions of nonlinear partial differential equations in complex domains. (English) Zbl 1152.35015
Reviewer: Yoshitsugu Takei (Kyoto)
Topological construction of transseries and introduction to generalized Borel summability. (English) Zbl 1072.40004
Costin, O. (ed.) et al., Analyzable functions and applications. International workshop, Edinburgh, UK, June 17–21, 2002. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3419-3/pbk). Contemporary Mathematics 373, 137-175 (2005).
Reviewer: Vladimir P. Kostov (Nice)
Formally well-posed Cauchy problems for linear partial differential equations with constant coefficients. (English) Zbl 1076.35030
Costin, O. (ed.) et al., Analyzable functions and applications. International workshop, Edinburgh, UK, June 17–21, 2002. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3419-3/pbk). Contemporary Mathematics 373, 87-102 (2005).
Asymptotic existence theorems for formal power series whose coefficients satisfy certain partial differential recursions. (English) Zbl 1144.34349
Recent progress in the theory of formal solutions for ODE and PDE. (English) Zbl 1054.34142
Reviewer: J. Saurer (Regensburg)
Multisummability of formal power series solutions of linear analytic \(q\)-difference equations. (Multisommabilité des séries entières solutions formelles d’une équation aux \(q\)-différences linéaire analytique.) (French) Zbl 1063.39001
Formal power series and linear systems of meromorphic ordinary differential equations. (English) Zbl 0942.34004
Universitext. New York, NY: Springer. xviii, 299 p. (2000).
Reviewer: A.Klíč (Praha)
Multisummability of complete formal solutions for nonlinear systems of meromorphic ordinary differential equations. (English) Zbl 0909.34002
Reviewer: N.Hayek (La Laguna)
On index theorems for linear ordinary differential operators. (English) Zbl 0901.34012
Reviewer: N.V.Grigorenko (Kyïv)
Moment methods and formal power series. (English) Zbl 0870.40002
Reviewer: K.Najzar (Praha)
Necessary and sufficient conditions for matrix summability methods to be stronger than multisummability. (English) Zbl 0864.34003
Matrix summation methods and multisummability. (Matrix-Summationsverfahren und Multisummierbarkeit.) (German) Zbl 0848.40004
Ulm: Univ. Ulm, Fak. f. Math. u. Wirtschaftswiss. 94 p. (1995).
Reviewer: H.H.Körle (Marburg)
Formal and numerical processes of summation of series solutions of differential equations. (Procédés formels et numériques de sommation de séries solutions d’équations différentielles.) (French) Zbl 0831.34003
Reviewer: H.Haruki (Waterloo/Ontario)
Divergent series, multisummability, and complex differential equations. (English) Zbl 0874.34002
Laine, Ilpo (ed.), Value distribution theory and complex differential equations. Papers from the workshop, Joensuu, Finland, September 18-21, 1994. Joensuu: University of Joensuu. Publ. Sci., Univ. Joensuu. 35, 1-16 (1995).
Reviewer: W.Balser (Ulm)
A new proof of summability of formal solutions of nonlinear meromorphic differential equations. (English) Zbl 0812.34005
Convergence of formal solutions of meromorphic differential equations containing parameters. (English) Zbl 0814.34008
Reviewer: F.M.Ragab (Cairo)
Normal forms and Stokes multipliers of nonlinear meromorphic differential equations. (English) Zbl 0794.34009
Tournier, E. (ed.), Computer algebra and differential equations. Selected papers of the third biennial workshop on computer algebra and differential equations held Marseille, France, June 1-5, 1992 (CADE-92). Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 193, 239-259 (1994).
Reviewer: H.Haruki (Waterloo / Ontario)
Multisummability of iterated integrals. (English) Zbl 0787.30026
Reviewer: W.Balser (Ulm)
MSC:
30E15
Multisummability of formal power series solutions of nonlinear meromorphic differential equations. (English) Zbl 0759.34003
Reviewer: B.L.J.Braaksma (Groningen)
Multisummable functions. (Fonctions multisommables.) (French) Zbl 0759.34007
Reviewer: J.-P.Ramis (Strasbourg)
Resummation of formal power series and orthogonal polynomials. (English) Zbl 0831.65076
Brezinski, Claude (ed.) et al., Orthogonal polynomials and their applications. Proceedings of the third international symposium held in Erice, Italy, June 1-8, 1990. Basel: J. C. Baltzer, IMACS Ann. Comput. Appl. Math. 9, 397-400 (1991).
Multisummability of formal power series solutions of linear ordinary differential equations. (English) Zbl 0754.34057
Reviewer: H.S.Nur (Fresno)
Multisummability and Stokes multipliers of linear meromorphic differential equations. (English) Zbl 0729.34005
Reviewer: W.Bergweiler (Aachen)
MSC:
34M99
Elementary acceleration and multisummability. I. (English) Zbl 0748.12005
Reviewer: N.V.Grigorenko (Kiev)
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