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Holomorphic functions of exponential type and duality for stein groups with algebraic connected component of identity

- S. Akbarov
- Mathematics
- 19 June 2008

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 component… Expand

Stereotype locally convex spaces

- S. Akbarov
- Mathematics
- 31 August 2000

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 important… Expand

Smooth structure and differential operators on a locally compact group

- S. Akbarov
- Mathematics
- 28 February 1995

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

- S. Akbarov
- Mathematics
- 10 October 2011

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 topological… Expand

Pontryagin Duality in the Theory of Topological Vector Spaces and in Topological Algebra

- S. Akbarov
- Mathematics
- 2003

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. This… Expand

Stereotype approximation property for the algebras $C(M)$ of continuous functions on metric spaces

- S. Akbarov
- Mathematics
- 5 September 2019

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 ${\tt Ste}$ of… Expand

Stereotype algebras with reflection and the double commutant theorem

- S. Akbarov
- Mathematics
- 1 November 1999

Differential geometry and quantization on a?locally compact group

- S. Akbarov
- Mathematics
- 30 April 1995

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 G… Expand

$C^\infty$-envelopes of topological algebras

- S. Akbarov
- Physics
- 11 March 2013

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