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16
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 13 (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.
Vector measures on topological spaces
 Georgian Math. J
"... Abstract. Let X be a completely regular Hausdorff space, E a quasicomplete locally convex space, C(X) (resp. Cb(X)) the space of all (resp. all, bounded), scalarvalued continuous functions on X, and B(X) and B0(X) be the classes of Borel and Baire subsets of X. We study the spaces Mt(X,E), Mτ (X, ..."
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Abstract. Let X be a completely regular Hausdorff space, E a quasicomplete locally convex space, C(X) (resp. Cb(X)) the space of all (resp. all, bounded), scalarvalued continuous functions on X, and B(X) and B0(X) be the classes of Borel and Baire subsets of X. We study the spaces Mt(X,E), Mτ (X,E), Mσ(X,E) of tight, τsmooth, σsmooth, Evalued Borel and Baire measures on X. Using strict topologies, we prove some measure representation theorems of linear operators between Cb(X) and E and then prove some convergence theorems about integrable functions. Also, the Alexandrov’s theorem is extended to the vector case and a representation theorem about the orderbounded, scalarvalued, linear maps from C(X) is generalized to the vectorvalued linear maps.
Fast Complete Locally Convex Linear Topological Spaces
 Internat. J. Math and Math. Sci. 9
, 1986
"... ABSTRACT. This is a study of relationship between the concepts of Mackey, ultrabornological, bornological, barrelled, and infrabarrelled spaces and the concept of fast completeness. An example of a fast complete but not sequentially complete space is presented. KEY WORDS AND PHRASES. Locally convex ..."
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ABSTRACT. This is a study of relationship between the concepts of Mackey, ultrabornological, bornological, barrelled, and infrabarrelled spaces and the concept of fast completeness. An example of a fast complete but not sequentially complete space is presented. KEY WORDS AND PHRASES. Locally convex space, fast complete space, bornological
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.