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12
THE CHU CONSTRUCTION
, 1996
"... We take another look at the Chu construction and show how to simplify it by looking at ..."
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Cited by 12 (1 self)
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We take another look at the Chu construction and show how to simplify it by looking at
Laguerre entire functions and related locally convex spaces
 Complex Variables Theory Appl
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A GENERALIZED SECOND ORDER FRAME BUNDLE FOR FRÉCHET MANIFOLDS
"... Abstract. Working within the framework of Fréchet modelled infinite dimensional manifolds, we propose a generalized notion of second order frame bundle. We revise in this way the classical notion of bundles of linear frames of order two, the direct definition and study of which is problematic due to ..."
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Cited by 5 (4 self)
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Abstract. Working within the framework of Fréchet modelled infinite dimensional manifolds, we propose a generalized notion of second order frame bundle. We revise in this way the classical notion of bundles of linear frames of order two, the direct definition and study of which is problematic due to intrinsic difficulties of the space models. However, this new structure keeps all the fundamental characteristics of a frame bundle: It is a principal Fréchet bundle associated (differentially and geometrically) with the corresponding second order tangent bundle.
An analytic RiemannHilbert correspondence for semisimple Lie groups, Represent
 Theory
, 1974
"... Abstract. Geometric Representation Theory for semisimple Lie groups has two main sheaf theoretic models. Namely, through BeilinsonBernstein localization theory, HarishChandra modules are related to holonomic sheaves of D modules on the flag variety. Then the (algebraic) RiemannHilbert correspond ..."
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Abstract. Geometric Representation Theory for semisimple Lie groups has two main sheaf theoretic models. Namely, through BeilinsonBernstein localization theory, HarishChandra modules are related to holonomic sheaves of D modules on the flag variety. Then the (algebraic) RiemannHilbert correspondence relates these sheaves to constructible sheaves of complex vector spaces. On the other hand, there is a parallel localization theory for globalized HarishChandra modules—i.e., modules over the full semisimple group which are completions of HarishChandra modules. In particular, HechtTaylor and Smithies have developed a localization theory relating minimal globalizations of HarishChandra modules to group equivariant sheaves of D modules on the flag variety. The main purpose of this paper is to develop an analytic RiemannHilbert correspondence relating these sheaves to constructible sheaves of complex vector spaces and to discuss the relationship between this “analytic ” study of global modules and the preceding “algebraic ” study of the underlying HarishChandra modules.
SOME COMMENTS ON THE RHS FORMULATION OF RESONANCE SCATTERING.
, 2008
"... We discuss the validity of a formula concerning a relation between functionals in quantum resonance scattering, which is often used in the current literature. 1 Introduction. This paper is a contribution to the theory of resonance scattering in which we discuss the validity of some formulas and conc ..."
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We discuss the validity of a formula concerning a relation between functionals in quantum resonance scattering, which is often used in the current literature. 1 Introduction. This paper is a contribution to the theory of resonance scattering in which we discuss the validity of some formulas and concepts that appear in the current literature. This kind of formulas are usually derived formally and used directly. Thus, an interpreation of them from the point of view of mathematical rigor is
The Chu Construction
, 1996
"... . We take another look at the Chu construction and show how to simplify it by looking at it as a module category in a trivial Chu category. This simplifies the construction substantially, especially in the case of a nonsymmetric biclosed monoidal category. We also show that if the original category ..."
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. We take another look at the Chu construction and show how to simplify it by looking at it as a module category in a trivial Chu category. This simplifies the construction substantially, especially in the case of a nonsymmetric biclosed monoidal category. We also show that if the original category is accessible, then for any of a large class of "polynomiallike" functors, the category of coalgebras has cofree objects. 1. Introduction In a recent paper, I showed how the Chu construction, given originally in [Chu, 1979] for symmetric monoidal closed categories, could be adapted to monoidal biclosed (but not necessarily symmetric) categories. The construction, although well motivated by the necessity of providing a doubly infinite family of duals, was rather complicated with many computations involving indices. Recently I have discovered that the autonomous structure of Chu categories can be put into the familiar context of bimodules over a not necessarily commutative "algebra" objec...
A CoordinateFree Foundation For Projective Spaces Treating Projective Maps From A Subset Of A Vector Space Into Another Vector Space
 Washington State University
, 1999
"... this paper was the problem of determining which maps on subsets of (not necessarily finite dimensional) vector spaces were "projective ". In view of the development of x2 through x4, the setting of this problem can be reduced to a function oe which is defined on a subset of a standard vect ..."
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this paper was the problem of determining which maps on subsets of (not necessarily finite dimensional) vector spaces were "projective ". In view of the development of x2 through x4, the setting of this problem can be reduced to a function oe which is defined on a subset of a standard vector space V of P , and which has a standard vector subspace X of another projective space R as its range. If such a function oe is the restriction of a projective isomorphism from P to R, it turns out that it must be the quotient of an affine map of V into X with an affine functional of V into F. A partial converse holds for a class of A FOUNDATION FOR PROJECTIVE SPACES AND PROJECTIVE MAPS 3 linear spaces which includes all locally convex spaces and finite dimensional vector spaces. These matters are treated in x5.
A Characterization Of ConvexityPreserving Maps From A Subset Of A Vector Space Into Another Vector Space
 J. London Math. Soc
, 1998
"... Let V and X be Hausdorff, locally convex, real, topological vector spaces with dimV ? 1. We show that a map oe from an open, connected subset of V onto an open subset of X is homeomorphic and convexitypreserving if and only if oe is projective. 1. Introduction The motivation for this paper is the ..."
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Let V and X be Hausdorff, locally convex, real, topological vector spaces with dimV ? 1. We show that a map oe from an open, connected subset of V onto an open subset of X is homeomorphic and convexitypreserving if and only if oe is projective. 1. Introduction The motivation for this paper is the role that certain projective maps play in the derivations of the wellpublicized algorithm of Karmarkar [7] (see also [6] and many references contained therein) for linear programming, and in the equally innovative but less well known class of algorithms of Davidon [3, 4, 5] for minimization of smooth nonlinear functions of several variables. Ariyawansa, Davidon and McKennon [1] examine the specific projective maps used in the derivations of the algorithms of Karmarkar [7] and Davidon [3, 4, 5]. They argue that as a consequence of the characterization of projective maps presented in this paper, projective maps are perhaps the only maps that are likely to be useful in the setting in which pr...
General Equilibrium, Wariness and Bubbles ∗
"... Faculdade de Economia, Universidade Nova de Lisboa, Portugal. Abstract: We say that a consumer is wary if she overlooks gains but not losses in remote sets of dates or states. We formulate this by requiring preferences to be upper but not lower Mackey semicontinuous and Bewley’s result on existence ..."
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Faculdade de Economia, Universidade Nova de Lisboa, Portugal. Abstract: We say that a consumer is wary if she overlooks gains but not losses in remote sets of dates or states. We formulate this by requiring preferences to be upper but not lower Mackey semicontinuous and Bewley’s result on existence of ArrowDebreu equilibrium whose prices are not necessarily countably additive holds. We relate wariness to some concepts studied in decision theory like lack of myopia and ambiguity aversion. Wary infinite lived agents are not impatient, have optimality conditions, in the form of weaker transversality conditions, that allow them to be creditors at infinity and bubbles occur for positive net supply assets completing the markets. In a two date economy, with infinite states, wary agents are not myopic and bubbles occur, as asset prices do not have to equal the series of returns weighted by state prices. A large class of efficient allocations can only be implemented with asset bubbles. Pessimistic attitudes lead agents to overvalue assets or durable goods with hedging properties, like gold.