Uniqueness and Free Interpolation for Logarithmic Potentials and the Cauchy Problem for the Laplace Equation in R2.
J. Bourgain, A. Aleksandrov, V. Havin (1995)
Geometric and functional analysis
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J. Bourgain, A. Aleksandrov, V. Havin (1995)
Geometric and functional analysis
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R. E. Lewkowicz (1988)
Colloquium Mathematicae
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Ioana Cioranescu, Hernan R. Henriques (1994)
Aequationes mathematicae
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E.M. Stein (1983)
Inventiones mathematicae
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J.H. Curtiss (1964/65)
Mathematische Zeitschrift
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Stephen Semmes (1988)
Revista Matemática Iberoamericana
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In recent years the study of interpolation of Banach spaces has seen some unexpected interactions with other fields. (...) In this paper I shall discuss some more interactions of interpolation theory with the rest of mathematics, beginning with some joint work with Coifman [CS]. Our basic idea was to look for the methods of interpolation that had interesting PDE's arising as examples.
S. Ugniewski (1977)
Applicationes Mathematicae
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Anders Olofsson (2004)
Studia Mathematica
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An operator-valued multi-variable Poisson type integral is studied. In Section 2 we obtain a new equivalent condition for the existence of a so-called regular unitary dilation of an n-tuple T=(T₁,...,Tₙ) of commuting contractions. Our development in Section 2 also contains a new proof of the classical dilation result of S. Brehmer, B. Sz.-Nagy and I. Halperin. In Section 3 we turn to the boundary behavior of this operator-valued Poisson integral. The results obtained in this section...
S. Hartman (1968)
Colloquium Mathematicae
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Irina Georgieva, Clemens Hofreither, Christoph Koutschan, Veronika Pillwein, Thotsaporn Thanatipanonda (2013)
Open Mathematics
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Given information about a harmonic function in two variables, consisting of a finite number of values of its Radon projections, i.e., integrals along some chords of the unit circle, we study the problem of interpolating these data by a harmonic polynomial. With the help of symbolic summation techniques we show that this interpolation problem has a unique solution in the case when the chords form a regular polygon. Numerical experiments for this and more general cases are presented. ...
Branga, Adrian (1998)
General Mathematics
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Mats Andersson, Mikael Passare (1991)
Mathematische Zeitschrift
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S. Paszkowski (1971)
Applicationes Mathematicae
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