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Holomorphic functions of exponential type and duality for stein groups with algebraic connected component of identity
We suggest a generalization of Pontryagin duality from the category of commutative, complex Lie groups to the category of (not necessarily commutative) Stein groups with algebraic connected componentExpand
Stereotype locally convex spaces
We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have importantExpand
Smooth structure and differential operators on a locally compact group
We describe the structure of differential operators (that is, locally linear operators in the space of Bruhat smooth functions) on an arbitrary locally compact group G.
Envelopes and refinements in categories, with applications to functional analysis
An envelope in a category is a construction that generalizes the operations of "exterior completion", like completion of a locally convex space, or Stone-\v{C}ech compactification of a topologicalExpand
Envelopes and imprints in categories
Pontryagin Duality in the Theory of Topological Vector Spaces and in Topological Algebra
The theory of topological vector spaces (TVS), being a foundation of modern functional analysis, is now considered as a completely mature, or, to be more specific, dead mathematical discipline. ThisExpand
Stereotype approximation property for the algebras $C(M)$ of continuous functions on metric spaces
In his previous works the author introduced the notion of the stereotype approximation property as an analog of the classical approximation property transferred to the category ${\tt Ste}$ ofExpand
Differential geometry and quantization on a?locally compact group
For an arbitrary locally compact group G, we describe the structure of the Lie algebra χ(G) of vector fields, the exterior algebra Λ(G) of differential forms, and the Poisson algebra of symbols on GExpand
$C^\infty$-envelopes of topological algebras