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Staff Introduction

NOMURA, Takaaki / Professor

My research area is analysis on domains, spaces or manifolds which admit Lie group actions. Recent interests are in Siegel domains in complex Euclidean spaces. These domains are multi-variable or matrix-variable generalizations of the usual upper half-plane in the complex plane. Current emphasis of the research is put on analytic and geometric characterizations of symmetric domains in the category of homogeneous Siegel domains. However, in the future, I plan to investigate representation-theoretic decomposition (e.g. irreducible decomposition) of various function spaces on the domain, and also to construct Fourier analysis on Siegel domains that includes well-developed Fourier analysis on symmetric spaces. Making good use of non-associative algebra structure which is geometrically introduced in the tangent space as well as of the Lie algebras of the Lie groups, I would like to weave the harmony produced by the interplay of geometry and analysis.  

Keywords Geometric Harmonic Analysis, Homogeneous Siegel Domains, Non-associative Algebras
Faculty , Department Faculty of Mathematics , Department of Mathematics