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European Mathematical Society Publishing House
2024-03-29 08:13:17
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PRIMS&vol=36&iss=6&update_since=2024-03-29
Publications of the Research Institute for Mathematical Sciences
Publ. Res. Inst. Math. Sci.
PRIMS
0034-5318
1663-4926
General
10.4171/PRIMS
http://www.ems-ph.org/doi/10.4171/PRIMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© Research Institute for Mathematical Sciences, Kyoto University
36
2000
6
Singularities at Infinity and their Vanishing Cycles, II. Monodromy
Dirk
Siersma
Universiteit Utrecht, UTRECHT, NETHERLANDS
Mihai
Tibăr
Université Lille I, VILLENEUVE D'ASCQ CEDEX, FRANCE
Topology of polynomial functions, singularities at infinity, relative monodromy
Let f : ℂn —> ℂ be any polynomial function. By using global polar methods, we introduce models for the fibers of f and we study the monodromy at atypical values of f, including the value infinity. We construct a geometric monodromy with controlled behavior and define global relative monodromy with respect to a general linear form. We prove localization results for the relative monodromy and derive a zeta-function formula for the monodromy around an atypical value. We compute the relative zeta function in several cases and emphasize the differences to the “classical” local situation.
Several complex variables and analytic spaces
General
659
679
10.2977/prims/1195139641
http://www.ems-ph.org/doi/10.2977/prims/1195139641
Morphisms of Certain Banach C*-Modules
Fabio
Bagarello
Università degli Studi di Palermo, PALERMO, ITALY
Camillo
Trapani
Università degli Studi di Palermo, PALERMO, ITALY
Morphisms and representations of a class of Banach C*-modules, called CQ*-algebras, are considered. Together with a general method for constructing CQ*-algebras, two different ways of extending the GNS-representation are presented.
Functional analysis
General
681
705
10.2977/prims/1195139642
http://www.ems-ph.org/doi/10.2977/prims/1195139642
Hilbert Space Theory for Reflectionless Relativistic Potentials
Simon
Ruijsenaars
Centre for Mathematics and Computer Science, AMSTERDAM, NETHERLANDS
We study Hilbert space aspects of explicit eigenfunctions for analytic difference operators that arise in the context of relativistic two-particle Calogero–Moser systems. We restrict attention to integer coupling constants g/ℏ, for which no reflection occurs. It is proved that the eigenfunction transforms are isometric, provided a certain dimensionless parameter a varies over a bounded interval (0,amax), whereas isometry is shown to be violated for generic a larger than amax. The anomaly is encoded in an explicit finite-rank operator, whose rank increases to ∞ as a goes to ∞.
Quantum theory
Special functions
Operator theory
General
707
753
10.2977/prims/1195139643
http://www.ems-ph.org/doi/10.2977/prims/1195139643