- 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