Japanese journal of mathematics. New series

Spherical matrix functions and Banach representability for locally compact motion groups

Hitoshi SHIN'YA

2002 Volume 28 Issue 2 Pages 163-201
Published: 2002
Released on J-STAGE: December 16, 2008

DOIhttps://doi.org/10.4099/math1924.28.163

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Radical hilbertien et tour localement cyclotomique

JEAN-FRANÇOIS JAULENT, CHRISTIAN MAIRE

2002 Volume 28 Issue 2 Pages 203-213
Published: 2002
Released on J-STAGE: December 16, 2008

DOIhttps://doi.org/10.4099/math1924.28.203

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We determine the module of relations of the Galois group of the maximal locally cyclotomic pro-e-extension of a number field K using the hilbertian radical of this field.

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Maslov index in the infinite dimension and a splitting formula for a spectral flow

Kenro FURUTANI, Nobukazu OTSUKI

2002 Volume 28 Issue 2 Pages 215-243
Published: 2002
Released on J-STAGE: December 16, 2008

DOIhttps://doi.org/10.4099/math1924.28.215

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First, we prove a local spectral flow formula (Theorem 3.7) for a differentiable curve of selfadjoint Fredholm operators. This formula enables us to prove in a simple way a general spectral flow formula (Theorem 3.$) which was already proved in [BF1]. Secondly, we prove a splitting formula (Theorem 4.12) for the spectral flow of a curve of selfadjoint elliptic operators on a closed manifold, which we decompose into two parts with commom boundary. Then the formula says that the spectral flow is a sum of two spectral flows on each part of the separated manifold with naturally introduced elliptic boundary conditions. In the course of proving this formula, we investigate a property of the Maslov index for paths of Fredholm pairs of Lagrangian subspaces.

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Zero sets of holomorphic functions in the Nevanlinna type class on convex domains in C²

Heungju AHN, Hong Rae CHO

2002 Volume 28 Issue 2 Pages 245-260
Published: 2002
Released on J-STAGE: February 08, 2010

DOIhttps://doi.org/10.4099/math1924.28.245

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We study a problem concerning zero sets of holomorphic functions in the Nevanlinna type class on convex domains (not necessarily finite type) in C². We give a Blaschke type condition for the zero set defined by a function in the Nevanlinna type class on convex domains in C². Moreover, we present an example of a convex domain of exponentially-flat infinite type on which it is possible to give sufficient conditions for zero sets of holomorphic functions in the classical Nevanlinna class.

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Lifschitz tail of a random Pauli Hamiltonian with an anomalous magnetic moment

Naomasa UEKI

2002 Volume 28 Issue 2 Pages 261-286
Published: 2002
Released on J-STAGE: December 16, 2008

DOIhttps://doi.org/10.4099/math1924.28.261

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Cobordism groups of special generic functions and groups of homotopy spheres

Osamu SAEKI

2002 Volume 28 Issue 2 Pages 287-297
Published: 2002
Released on J-STAGE: December 16, 2008

DOIhttps://doi.org/10.4099/math1924.28.287

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Morse functions with only minima and maxima as their critical points are called special generic functions. We show that for n greater than or equal to 6, the n-dimensional oriented cobordism group of such functions is naturally isomorphic to the h-cobordism group of oriented homotopy n-spheres. We also study the unoriented cobordism group of special generic functions.

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Hopf-equivalences for zero-dimensional dynamical systems

Hisatoshi YUASA

2002 Volume 28 Issue 2 Pages 299-312
Published: 2002
Released on J-STAGE: December 16, 2008

DOIhttps://doi.org/10.4099/math1924.28.299

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In the class of zero-dimensional dynamical systems, we see some links among Hopf-equivalences, coboundaries, hitting times and recurrence properties for dynamical systems. Each of the first three notions concerns with a relation between an arbitrary pair of nonempty clopen sets.

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