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1
Content available remote

Covariant differential operators and Green's functions

100%
Engliš M., Peetre J.
Annales Polonici Mathematici
|
1997
|
tom 66
|
nr 1
77-103
EN
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 𝔻 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 𝜟. 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 𝜟 : the former is up to conjugation a polynomial of the latter.
2
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Extreme points of the complex binary trilinear ball

81%
Cobos F., Kühn T., Peetre J.
Studia Mathematica
|
2000
|
tom 138
|
nr 1
81-92
EN
We characterize all the extreme points of the unit ball in the space of trilinear forms on the Hilbert space $ℂ^2$. This answers a question posed by R. Grząślewicz and K. John [7], who solved the corresponding problem for the real Hilbert space $ℝ^2$. As an application we determine the best constant in the inequality between the Hilbert-Schmidt norm and the norm of trilinear forms.
3
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A new look on Hankel forms over Fock space

60%
Janson S., Peetre J., Wallstén R.
Studia Mathematica
|
1989-1990
|
tom 95
|
nr 1
33-41
4
Content available remote

A multidimensional Wolff theorem

41%
Cobos F., Peetre J.
Studia Mathematica
|
1989
|
tom 94
|
nr 3
273-290
5
Content available remote

Interpolation of Orlicz spaces

41%
Gustavsson J., Peetre J.
Studia Mathematica
|
1977
|
tom 60
|
nr 1
33-59
6
Content available remote

A new approach in interpolation spaces

40%
Peetre J.
Studia Mathematica
|
1970
|
tom 34
|
nr 1
23-42
7
Content available remote

Locally analytically pseudo-convex topological vector spaces

40%
Peetre J.
Studia Mathematica
|
1982
|
tom 73
|
nr 3
253-262
8
Content available remote

Estimates for eigenfunctions

35%
Peetre J.
Studia Mathematica
|
1966-1967
|
tom 28
|
nr 2
169-182
9
Content available remote

Two observations on a theorem by Coifman

35%
Peetre J.
Studia Mathematica
|
1979
|
tom 64
|
nr 3
191-194
10
Content available remote

Properties of the L function

31%
Gustavsson J., Peetre J.
Studia Mathematica
|
1982
|
tom 74
|
nr 2
105-121
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