TY - JOUR
A1 - Cerejeiras, Paula
A1 - Kähler, Uwe
A1 - Legatiuk, Anastasiia
A1 - Legatiuk, Dmitrii
T1 - Discrete Hardy Spaces for Bounded Domains in Rn
JF - Complex Analysis and Operator Theory
N2 - Discrete function theory in higher-dimensional setting has been in active development since many years. However, available results focus on studying discrete setting for such canonical domains as half-space, while the case of bounded domains generally remained unconsidered. Therefore, this paper presents the extension of the higher-dimensional function theory to the case of arbitrary bounded domains in Rn. On this way, discrete Stokes’ formula, discrete Borel–Pompeiu formula, as well as discrete Hardy spaces for general bounded domains are constructed. Finally, several discrete Hilbert problems are considered.
KW - Dirac-Operator
KW - Randwertproblem
KW - Funktionentheorie
KW - discrete Dirac operator
KW - discrete monogenic functions
KW - discrete boundary value problems
Y1 - 2020
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210804-44746
UR - https://link.springer.com/article/10.1007/s11785-020-01047-6
VL - 2021
IS - Volume 15, article 4
SP - 1
EP - 32
PB - Springer
CY - Heidelberg
ER -
TY - CHAP
A1 - Cerejeiras, Paula
T1 - Hyperbolic Qp-scales
N2 - The Qp-scales were first introduced in [1] as interpolation spaces between the Bloch and Dirichlet spaces in the complex space. ... However, such treatment presents the disadvantage of only considering the Euclidean case. In order to obtain an approach to homogeneous hyperbolic manifolds, the projective model of Gel'fand was retaken in [2]. With the help of a convenient fundamental solution for the hyperbolic (homogeneous of degree ®) D® (see [5]) it was introduced in [7] and [3] equivalent Qp scales for homogeneous hyperbolic spaces. In this talk we shall present and study some properties of this hyperbolic scale.
KW - Quaternion
Y1 - 2003
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-2853
ER -
TY - CHAP
A1 - Ebert, Svend
A1 - Bernstein, Swanhild
A1 - Cerejeiras, Paula
A1 - Kähler, Uwe
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - NONZONAL WAVELETS ON S^N
N2 - In the present article we will construct wavelets on an arbitrary dimensional sphere S^n due the approach of approximate Identities. There are two equivalently approaches to wavelets. The group theoretical approach formulates a square integrability condition for a group acting via unitary, irreducible representation on the sphere. The connection to the group theoretical approach will be sketched. The concept of approximate identities uses the same constructions in the background, here we select an appropriate section of dilations and translations in the group acting on the sphere in two steps. At First we will formulate dilations in terms of approximate identities and than we call in translations on the sphere as rotations. This leads to the construction of an orthogonal polynomial system in L²(SO(n+1)). That approach is convenient to construct concrete wavelets, since the appropriate kernels can be constructed form the heat kernel leading to the approximate Identity of Gauss-Weierstra\ss. We will work out conditions to functions forming a family of wavelets, subsequently we formulate how we can construct zonal wavelets from a approximate Identity and the relation to admissibility of nonzonal wavelets. Eventually we will give an example of a nonzonal Wavelet on $S^n$, which we obtain from the approximate identity of Gauss-Weierstraß.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Architektur
KW - Computerunterstütztes Verfahren
KW - Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing
Y1 - 2010
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28406
UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN - 1611-4086
ER -