arXiv subjects
Publications and source records attributed to Shigeru Yamagami.
We supplement the Herglotz-Nevanlinna integral representation of so-called Pick functions by adding the formula for Möbius transforms and the positivity characterization near boundary supports.
In connection with the Herglotz-Nevanlinna integral representation of so-called Pick functions, we introduce the notion of boundary measure of holomorphic functions on the imaginary domain and elucidate some of basic properties.
Radial representations of finitely generated free groups are studied. The associated C*-algebra is located between the reduced and full group C*-algebras and its primitive ideal space is described concretely as a topological space.
Related to radial functions on free groups, we focus on certain polynomial hypergroups and work out spectral analysis with the help of the Stieltjes transform of their analytic functionals.
We present a replacement for traditional Riemann integrals in undergraduate calculus, which supplements naive precalculus and at the same time opens a way to more sophisticated theories such as Lebesgue integration.
In the framework of continued fraction expansions of Stieltjes transforms, we consider shifting of semicircular laws. The continuous part of the associated measure admits a density function which is the quotient of semicircular one by a polynomial. We study how this polynomial denominator determines shifted semicircular laws, with explicit descriptions in examples of shifting up to the level of step two.
A system of matrix units in the Weyl algebra of convolution type is constructed with the aid of a Gaussian element so that it includes von Neumann's minimal projection, which explicitly shows that the associated C*-algebra is a compact operator algebra. The spectral decomposition of an arbitrary Gaussian element is then worked out in terms of the diagonal projections in the matrix units.
In connection with parametric rescaling of free dynamics of CCR, we introduce a flow on the set of covariance forms and investigate its thermodynamic behavior at low temperature with the conclusion that every free state approaches to a selected Fock state as a limit.
Categories of W*-bimodules are shown in an explicit and algebraic way to constitute an involutive W*-bicategory.
Trace formulas are investigated in non-commutative integration theory. The main result is to evaluate the standard trace of a Takesaki dual and, for this, we introduce the notion of interpolator and accompanied boundary objects. The formula is then applied to explore a variation of Haagerup's trace formula.
C.Swartz' result on tensor product measures is reviewed with proofs from the scratch.
We shall discuss how the notions of multicategories and their linear representations are related with tensor categories. When one focuses on the ones arizing from planar diagrams, it particularly implies that there is a natural one-to-one correspondence between planar algebras and singly generated bicategories.
Two quasi-free states on a CAR or CCR algebra are shown to generate quasi-equivalent representations unless they are disjoint.
Geometric positions of square roots of coherent states of CCR algebras are investigated along with an explicit formula for transition amplitudes among them, which is a natural extension of our previous results on quasifree states and will provide a new insight into quasi-equivalence problems of quasifree states.
Geometric positions of square roots of quasi-free states of CCR algebras are investigated together with an explicit formula for transition amplitudes among them.
The transition amplitude between square roots of states, which is an analogue of Hellinger integral in classical measure theory, is investigated in connection with operator-algebraic representation theory. A variational expression based on geometric mean of positive forms is utilized to obtain an approximation formula for transition amplitudes.
The tensor categories of oriented Kauffman diagrams are studied with description of fiber functors on them as well as the associated Hopf algebras.
Fiber functors on Temperley-Lieb categories are investigated with the help of classification results on non-degenerate bilinear forms. The case of unitary fiber functors is also considered.