Temat: Cauchy function - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Homogeneous extremal function for a ball in ℝ²
Autorzy:: Baran, Mirosław
Powiązania:: https://bibliotekanauki.pl/articles/1294104.pdf
Data publikacji:: 1999
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: homogeneous extremal function
Cauchy-Poisson transform
Opis:: We point out relations between Siciak's homogeneous extremal function $Ψ_B$ and the Cauchy-Poisson transform in case $B$ is a ball in ℝ². In particular, we find effective formulas for $Ψ_B$ for an important class of balls. These formulas imply that, in general, $Ψ_B$ is not a norm in ℂ².
Źródło:: Annales Polonici Mathematici; 1999, 71, 2; 141-150
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: A weighted Plancherel formula II. The case of the ball
Autorzy:: Zhang, Genkai
Powiązania:: https://bibliotekanauki.pl/articles/1293186.pdf
Data publikacji:: 1992
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: Plancherel formula
Harish-Chandra c-function
reproducing kernel
orthogonal polynomial
invariant Cauchy-Riemann operator
Opis:: The group SU(1,d) acts naturally on the Hilbert space $L²(B dμ_α) (α > -1)$, where B is the unit ball of $ℂ^d$ and $dμ_α$ the weighted measure $(1-|z|²)^α dm(z)$. It is proved that the irreducible decomposition of the space has finitely many discrete parts and a continuous part. Each discrete part corresponds to a zero of the generalized Harish-Chandra c-function in the lower half plane. The discrete parts are studied via invariant Cauchy-Riemann operators. The representations on the discrete parts are equivalent to actions on some holomorphic tensor fields.
Źródło:: Studia Mathematica; 1992, 102, 2; 103-120
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Covariant differential operators and Greens functions
Autorzy:: Engliš, Miroslav
Peetre, Jaak
Powiązania:: https://bibliotekanauki.pl/articles/1294789.pdf
Data publikacji:: 1997
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: covariant differential operator
Laplace operator
Green's function
Hayman-Korenblum fomula
Bojarski's theorem
Bol's lemma
covariant Cauchy-Riemann operator
dilogarithm
trilogarithm
general nonsense
Opis:: The basic idea of this paper is to use the covariance of a partial differential operator under a suitable group action to determine suitable associated Green's functions. For instance, we offer a new proof of a formula for Green's function of the mth power $Δ^m$ of the ordinary Laplace's operator Δ in the unit disk found in a recent paper (Hayman-Korenblum, J. Anal. Math. 60 (1993), 113-133). We also study Green's functions associated with mth powers of the Poincaré invariant Laplace operator . It turns out that they can be expressed in terms of certain special functions of which the dilogarithm (m = 2) and the trilogarithm (m = 3) are the simplest instances. Finally, we establish a relationship between $Δ^m$ and : the former is up to conjugation a polynomial of the latter.
Źródło:: Annales Polonici Mathematici; 1997, 66, 1; 77-103
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

Artykuł

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