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)
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Counterexamples to Hölmgren's uniqueness for analytic non linear Cauchy problem.
G. Métivier (1993)
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Rectifiability, analytic capacity, and singular integrals.
Mattila, Pertti (1998)
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Angus E. Taylor (1937)
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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.
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Koh, E.K., Li, C.K. (1993)
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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)
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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)
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Analytic capacity, Calderón-Zygmund operators, and rectifiability
Guy David (1999)
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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.