Journal ArticleDOI
Analysis in or the principal function theory
TLDR
In this paper, a function theory connected with principal series representation of the discrete series was explored in contrast to standard complex analysis connected with discrete series, and the Hardy space, Cauchy-Riemann equation and Taylor expansion were constructed.Abstract:
We explore a function theory connected with the principal series representation of ) in contrast to standard complex analysis connected with the discrete series. We construct counterparts for the Cauchy integral formula, the Hardy space, the Cauchy-Riemann equation and the Taylor expansion.read more
Citations
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Calculus of operators: covariant transform and relative convolutions
TL;DR: In this paper, a covariant theory of operators related to groups and homogeneous spaces is presented, and a methodical use of groups and their rep- resentations allows to obtain results of algebraic and analytical nature.
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Erlangen Program at Large-1: Geometry of Invariants
TL;DR: In this paper, a geometrical foundation for a systematic treatment of three main (elliptic, parabolic and hyperbolic) types of analytic function theories based on the representation theory of SL 2 (R) group is presented.
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Two-dimensional conformal models of space-time and their compactification
TL;DR: In this article, the authors studied the geometry of two-dimensional models of conformal space-time based on the group of Mobius transformation and the natural geometric invariants, called cycles, are used to linearize Mobius action.
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Symmetry, Geometry, and Quantization with Hypercomplex Numbers
TL;DR: In this article, relations between quantum and classical mechanics are clarified in a framework based on induced representations which are built from complex-/dual-/double-valued characters, and a Calderon-Vaillancourt-type norm estimation for relative convolutions is presented.
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Projective Compactification of \(\mathbb {R}^{1,1}\) and Its Möbius Geometry
TL;DR: In this paper, the semi-Riemannian manifold is considered as a split complex plane and its conformal compactification as an analogue of the Riemann sphere is studied.
References
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Journal ArticleDOI
A Geometric Construction of the Discrete Series for Semisimple Lie Groups
Michael Atiyah,Wilfried Schmid +1 more
TL;DR: In the representation theory of compact groups, a major role is played by the Peter-Weyl theorem, which asserts that the regular representation L 2(K) decomposes as a countable direct sum of irreducibles with finite multiplicity as mentioned in this paper.
Journal ArticleDOI
Szegö Kernels Associated with Discrete Series.
Journal ArticleDOI
Möbius covariance of iterated Dirac operators
Jaak Peetre,Tao Qian +1 more
TL;DR: In this paper, a new conformal covatiance result for the iterated Dirac operators was given, based on the relationship between the fundamental solutions and the conformal weights.