Mihai Putinar
A Striktpositivstellensatz for measurable functions (corrected version).
Wed, 11/04/2009 - 16:01 — SomNambulAuthors: Mihai Putinar
Subjects: Functional Analysis
AbstractA weighted sums of squares decomposition of positive Borel measurable
functions on a bounded Borel subset of the Euclidean space is obtained via
duality from the spectral theorem for tuples of commuting self-adjoint
operators. The analogous result for polynomials or certain rational functions
was amply exploited during the last decade in a variety of applications.Positivity and optimization for semi-algebraic functions.
Thu, 10/29/2009 - 16:01 — SomNambulAuthors: Mihai Putinar, Jean-Bernard Lasserre
Subjects: Optimization and Control
AbstractWe describe algebraic certificates of positivity for functions belonging to a
finitely generated algebra of Borel measurable functions, with particular
emphasis to algebras generated by semi-algebraic functions. In which case the
standard global optimization problem with constraints given by elements of the
same algebra is reduced via a natural change of variables to the better
understood case of polynomial optimization. A collection of simple examples and
numerical experiments complement the theoretical parts of the article.Unitary invariants for Hilbert modules of finite rank.
Fri, 09/11/2009 - 19:12 — SomNambulAuthors: Shibananda Biswas, Gadadhar Misra, Mihai Putinar
Subjects: Spectral Theory
AbstractA refined notion of curvature for a linear system of Hermitian vector spaces,
in the sense of Grothendieck, leads to the unitary classification of a large
class of analytic Hilbert modules. Specifically, we study Hilbert sub-modules,
for which the localizations are of finite (but not constant) dimension, of an
analytic function space with a reproducing kernel.
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