Carleman’s Formulas in Complex Analysis: Theory and Applications

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Carleman formulas - Encyclopedia of Mathematics

B , Nicosia , Cyprus. Use the link below to share a full-text version of this article with your friends and colleagues. Learn more. An extensive survey of Carleman formulas is found in [AIZ]. In [AIZTV] we considered the simplest Carleman formulas in one and several complex variables on particular simply connected domains. This is a particular form of abstract Carleman formula, but it involves simply connected domains, not covered by previous results. Volume , Issue 1. The full text of this article hosted at iucr. If you do not receive an email within 10 minutes, your email address may not be registered, and you may need to create a new Wiley Online Library account.

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Aĭzenberg, L. A. (Lev Abramovich) 1937-2018

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Corresponding author. Received Dec 1; Accepted Aug 5. Then, the following diagram is commutative.

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Open in a separate window. The Carleman matrix Here, we construct a class of infinite matrices representing ordinary differential equations.

Normal form of a Carleman matrix In this section, we provide a definition of the normal form of a Carleman matrix. Proofs In this section, we provide proofs of the propositions introduced above. Proof of Proposition 2 Part 1. Remark 3 Another definition of a Weierstrass matrix may be introduced. Proof of Proposition 5 Part 1. Remark 4 Another definition for the Carleman matrix may be introduced.

ISBN 13: 9780792321217

Proof of Proposition 6 Step 1. Proof of Proposition 7 Step 1. Example In this section, we give an example of the algorithm introduced above. Results and discussion The algorithm presented here for constructing the normal form and normalizing transformation is based on Carleman linearization of differential equations 4 to the form 6 by 5.

Competing interests The author declares that he has no competing interests. References Arnold VI. Geometrical methods in the theory of ordinary differential equations. New York: Springer; The existence of the continuations and the representation of the solutions in celestial mechanics. Proc Inst Theor Astron.

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Adaptive control processes: a guided tour. Princeton: Princeton university press; Dynamical systems. Providence: American Mathematical Society; In: Giacaglia GEO, editor. Periodic orbits, stability and resonances.

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Dordrecht: Springer; Analytical techniques of celestial mechanics. Heidelberg: Springer; Construction of a general planetary theory of the first order. Celest Mech. Celest Mech Dyn Astron. Acta Math.

An algorithm for computing a new normal form for dynamical systems. J Symb Comput. Infinite systems method in the theory of normal forms for non-autonomous differential equations.

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Filtering of stochastic nonlinear differential systems via a Carleman approximation approach. Review of the works on the orbital evolution of solar system major planets.