The Cauchy problem and Hadamard's example
Jan Persson (1976)
Journées équations aux dérivées partielles
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Displaying similar documents to “A T(b) theorem with remarks on analytic capacity and the Cauchy integral”
The Cauchy problem and Hadamard's example
A remark concerning the dependence on the initial data of the solution of the Cauchy problem for a linear equation with analytic coefficients
H. Marcinkowska (1971)
Annales Polonici Mathematici
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Counterexamples to Hölmgren's uniqueness for analytic non linear Cauchy problem.
G. Métivier (1993)
Inventiones mathematicae
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Rectifiability, analytic capacity, and singular integrals.
Mattila, Pertti (1998)
Documenta Mathematica
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Singular sets of separately analytic functions
Józef Siciak (1990)
Colloquium Mathematicae
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Analytic functions in general analysis
Angus E. Taylor (1937)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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On a theorem of Cauchy-Kovalevskaya type for a class of nonlinear PDE's of higher order with deviating arguments
Antoni Augustynowicz (1999)
Annales Polonici Mathematici
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We prove an existence theorem of Cauchy-Kovalevskaya type for the equation where f is a polynomial with respect to the last k variables.
On defining the generalized functions and .
Koh, E.K., Li, C.K. (1993)
International Journal of Mathematics and Mathematical Sciences
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On the hyper-order of analytic solutions of linear differential equations near a finite singular point
Meryem Chetti, Karima Hamani (2024)
Mathematica Bohemica
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We study the hyper-order of analytic solutions of linear differential equations with analytic coefficients having the same order near a finite singular point. We improve previous results given by S. Cherief and S. Hamouda (2021). We also consider the nonhomogeneous linear differential equations.
Analytic and Gevrey Hypoellipticity
Luigi Rodino (1985)
Publications mathématiques et informatique de Rennes
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Analytic capacity, Calderón-Zygmund operators, and rectifiability
Guy David (1999)
Publicacions Matemàtiques
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For K ⊂ C compact, we say that K has vanishing analytic capacity (or γ(K) = 0) when all bounded analytic functions on CK are constant. We would like to characterize γ(K) = 0 geometrically. Easily, γ(K) > 0 when K has Hausdorff dimension larger than 1, and γ(K) = 0 when dim(K) < 1. Thus only the case when dim(K) = 1 is interesting. So far there is no characterization of γ(K) = 0 in general, but the special case when the Hausdorff measure H(K) is finite was recently settled....
An analytic characterization of the symmetric extension of a Herglotz-Nevanlinna function
Mitja Nedic (2023)
Czechoslovak Mathematical Journal
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We derive an analytic characterization of the symmetric extension of a Herglotz-Nevanlinna function. Here, the main tools used are the so-called variable non-dependence property and the symmetry formula satisfied by Herglotz-Nevanlinna and Cauchy-type functions. We also provide an extension of the Stieltjes inversion formula for Cauchy-type and quasi-Cauchy-type functions.