Harmonic Analysis on Double Coset Spaces

Multi-operator colligations and multivariate characteristic functions

In the spectral theory of non-self-adjoint operators there is a well-known operation of product of operator colligations. Many similar operations appear in the theory of infinite-dimensional groups as multiplications of double cosets. We construct characteristic functions for such double cosets and get semigroups of matrix-valued functions in matrix balls.

自由 nilspace、双陪集 nilspace 与 Gowers 范数

Free nilspaces, double-coset nilspaces, and Gowers norms

本文刻画紧有限秩及一般 $k$ 步紧 nilspace，证明其可由自由 nilspace 经高阶格作用取商并表示为双陪集空间，进而得到有限 Abel 群上 Gowers 范数的新逆定理。

Double algebraic genericity of universal harmonic functions on trees

It is well known that the set of universal functions on a tree contains a vector space except zero which is dense in the set of harmonic functions. In this paper we improve this result by proving that the set of universal functions on a tree contains two vector spaces except zero which are dense in the space of harmonic functions and intersect only at zero.

Double algebraic genericity of universal harmonic functions on trees in the general case

It has been shown that the set of universal functions on trees contains a linear subspace except zero, dense in the space of harmonic functions. In this paper we show that the set of universal functions contains two linear subspaces except zero, dense in the space of harmonic functions that intersect only at zero. We work in the most general case that has been studied so far, letting our functions take values over a topological vector space.