Uniformization and Constructive Analytic Continuation of Taylor Series
نویسندگان
چکیده
We analyze the problem of global reconstruction functions as accurately possible, based on partial information in form a truncated power series at some point, and additional analyticity properties. This situation occurs frequently applications. The question optimal procedure was open, we formulate it well-posed mathematical problem. Its solution leads to practical method which provides dramatic accuracy improvements over existing techniques. Our is uniformization Riemann surfaces. As an application, show that our can be implemented for solutions wide class nonlinear ODEs. find new method, use construct uniformizing maps needed special functions, including Painlevé equations $$P_\mathrm{I}$$ – $$P_{\mathrm{V}}$$ . also introduce rigorous constructive regularization, elimination singularities whose position type are known. If these unknown, same enables highly sensitive resonance determine singularity. In applications where less explicit available about surface, approach techniques lead approximate, but still much more precise methods than ones, especially vicinity singularities, points greatest interest.
منابع مشابه
Distributions and Analytic Continuation of Dirichlet Series
Dirichlet series and Fourier series can both be used to encode sequences of complex numbers an , n ∈ N. Dirichlet series do so in a manner adapted to the multiplicative structure of N, whereas Fourier series reflect the additive structure of N. Formally at least, the Mellin transform relates these two ways of representing sequences. In this paper, we make sense of the Mellin transform of period...
متن کاملThe Analytic Continuation of the Discrete Series
In this paper the analytic continuation of the holomorphic discrete series is defined. The most elementary properties of these representations are developed. The study of when these representations are unitary is begun.
متن کاملAnalytic Continuation of the Fibonacci Dirichlet Series
Functions defined by Dirichlet series J^=l a/f are Interesting because they often code and link properties of an algebraic nature in analytic terms. This is most often the case when the coefficients an are multiplicative arithmetic functions, such as the number or sum of the divisors of w, or group characters. Such series were the first to be studied, and are fundamental in many aspects of numb...
متن کاملAnalytic Continuation of the Principal Series
The purpose of this note is to announce results obtained in the analytic continuation of the (nondegenerate) "principal series" of representations of the nXn complex unimodular group. This study has as its starting point a similar one for the 2X2 real unimodular group previously carried out by us in [4]. We let G be the nXn complex unimodular group and C its diagonal subgroup consisting of elem...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2022
ISSN: ['0010-3616', '1432-0916']
DOI: https://doi.org/10.1007/s00220-022-04361-6