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The Analytic Principle of Continuity
The American Mathematical Monthly, 2005arguments with complex ones. We come across instances of the use of this device if we study the evolution of geometry beginning with Kepler. Most of the mathematicians who used this device referred to it as the principle of continuity (this term is sometimes also used in the sense of an axiom of continuity of a space, such as "Dedekind's Principle" or "
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An Algorithm for Analytic Continuation
SIAM Journal on Numerical Analysis, 1966Abstract : Let an analytic function f of a single complex variable be defined in a neighborhood of a point z sub 0 by means of its Taylor series at z sub 0. A constructive method is discussed for the solution of the following problem: Suppose it is known that the function f can be continued analytically into a domain of the complex plane. It is desired
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Analytic Continuation of Toeplitz Operators
The Journal of Geometric Analysis, 2014Let \(f(z)=\sum_\nu f_\nu z^\nu\) be a holomorphic function on the unit ball \({\mathbb B}^n\) in \({\mathbb C}^n\). For \(\alpha\in{\mathbb R}\), \textit{R.-H. Zhao} and \textit{K. Zhu} [Mém. Soc. Math. Fr., Nouv. Sér. 115, 1--103 (2008; Zbl 1176.32001)] considered \(\|f\|_{\alpha,\#}^2:=\sum_\nu\frac{\nu!}{|\nu|!}\frac{|f_\nu|^2}{(|\nu|+1)^{\alpha+n}}
Bommier-Hato, H. +2 more
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INVARIANT SUBSPACES OF ANALYTIC FUNCTIONS. ANALYTIC CONTINUATION
Mathematics of the USSR-Izvestiya, 1973Let G be a region in the complex plane; let H be the space of functions analytic in G with the topology of uniform convergence on compacta of G; let W be a nontrivial invariant (with respect to differentiation) subspace in H which admits a spectral synthesis.
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On the Continuability of Multivalued Analytic Functions to an Analytic Subset
Functional Analysis and Its Applications, 2001Let \(M\) be an analytic manifold and let \(\Sigma\) be an analytic subset of \(M\). Let \(b\in M\) and let \(f_b\) be a germ of an analytic function at \(b\) that can be continued analytically along any curve \(\gamma: [0,1]\to M\), \(\gamma(0) = b\), such that \(\gamma\) can intersect the set \(\Sigma\) at the initial instant only.
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A continuous dependence result in the analytic continuation problem
form, 1999Summary: We study the following problem. Consider an open, bounded and connected set \(\Omega\) in \(\mathbb{R}^n\) and an open subset \(E\) in \(\Omega\). Knowing the values of an analytic function \(f\) on \(E\) we want to find its value on \(\Omega\). The problem is not well posed in the sense of Hadamard.
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Simultaneous Analytic Continuation
Journal of the London Mathematical Society, 1959openaire +2 more sources
ON A GENERALIZED ANALYTIC CONTINUATION
Mathematics of the USSR-Sbornik, 1968openaire +2 more sources
On the error of analytical continuation in physical geodesy
Journal of Geodesy, 1996Lars E Sjoberg
exaly