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S. V. Ludkovsky

Publications and source records attributed to S. V. Ludkovsky.

48 records · Page 3Linked to original sources
arXiv2003

Stochastic processes on geometric loop and diffeomorphism groups of real and complex manifolds, associated unitary representations

Stochastic processes are considered on free loop spaces, geometric loop and diffeomorphism groups of real and complex manifolds. They are used for investigations of Wiener differentiable quasi-invariant measures on such groups relative to dense subgroups. There are considered finite-dimensional and also infinite-dimensional manifolds. Such measures are used for the investigation of associated unitary representations of these groups.

math.GR↗
arXiv2003

Hahn-Banach theorems for $κ$-normed spaces

For a new class of topological vector spaces, namely $κ$-normed spaces, and associated quasisemilinear topological preordered space is defined and investigated. This structure arise naturally from the consideration of a $κ$-norm, that is a distance function between a point and a $G_δ$-subset. For it, analogs of the Hahn-Banach theorem are proved.

math.FA↗
arXiv2002

Non-Archimedean stochastic processes on non-Archimedean manifolds

Stochastic processes on manifolds over non-Archimedean fields and with transition measures having values in the field $\bf C$ of complex numbers are defined and investigated. The analogs of Markov, Poisson and Wiener processes are studied. For Poisson processes the non-Archimedean analog of the Lèvy theorem is proved. Stochastic antiderivational equations as well as pseudodifferential equations on manifolds are investigated.

math.GM↗
arXiv2002

Differentiable functions of quaternion variables

We investigate differentiability of functions defined on regions of the real quaternion field and obtain a noncommutative version of the Cauchy-Riemann conditions. Then we study the noncommutative analog of the Cauchy integral as well as criteria for functions of a quaternion variable to be analytic. In particular, the quaternionic exponential and logarithmic functions are being considered. Main results include quaternion versions of Hurwitz' theorem, Mittag-Leffler's theorem and Weierstrass theorem.

math.CV↗
arXiv2001

Stochastic processes on non-Archimedean spaces. III. Stochastic processes on totally disconnected topological groups

Stochastic processes on totally disconnected topological groups are investigated. In particular they are considered for diffeomorphism groups and loop groups of manifolds on non-Archimedean Banach spaces. Theorems about a quasi-invariance and a pseudo-differentiability of transition measures are proved. Transition measures are used for the construction of strongly continuous representations including irreducible of these groups. In addition stochastic processes on general Banach-Lie groups, loop monoids, loop spaces and path spaces of manifolds on Banach spaces over non-Archimedean local fields also are investigated.

math.GM↗
arXiv2000

Absolute non-Archimedean polyhedral expansions of ultrauniform spaces

This work is devoted to the investigation of the problem about inverse mapping systems expansions of ultrauniform spaces $X$ using polyhedra over non-Archimedean locally compact fields $\bf L$. Theorems about expansions of complete ultrametric and ultrauniform spaces are proved. Absolute polyhedral expansions and inverse mapping systems of expansions for non-complete spaces are investigated. This article also contains results about a relation of $dim (X)$ and dimensions of polyhedra over $\bf L$.

math.AT↗
arXiv2000

A structure and representations of diffeomorphism groups of non-Archimedean manifolds

Diffeomorphism groups $G$ of manifolds $M$ on locally $\bf F$-convex spaces over non-Archimedean fields $\bf F$ are investigated. It is shown that their structure has many differences with the diffeomorphism groups of real and complex manifolds. It is proved that $G$ is not a Banach-Lie group, but it has a neighbourhood $W$ of the unit element $e$ such that each element $g$ in $W$ belongs to at least one corresponding one-parameter subgroup. It is proved that $G$ is simple and perfect. Its compact subgroups $G_c$ are studied such that a dimension over $\bf F$ of its tangent space $dim_{\bf F}T_eG_c$ in $e$ may be infinite. This is used for decompositions of continuous representations into irreducible and investigations of induced representations.

math.GR↗
arXiv1999

Poisson measures for topological groups and their representations

Gaussian quasi-invariant measures on groups of diffeomorphisms and loop groups G relative to dense subgroups G' were constructed. In the non-Archimedean case the wider class of measures was investigated, than in the real case. The cases of Riemann and non-Archimedean manifolds were considered. This article is related with unitary representations of G' associated with Poisson measures on $G^{\bf N}$ and uses quasi-invariant measures on G from the previous works. Several groups are considered: (1) (a) diffeomorphisms and (b) loop groups of real manifolds, (2) (a) diffeomorphisms and (b) loop groups of non-Archimedean manifolds over local fields. Besides these four cases further the fifth and the sixth cases are considered: for (3) (a) real and (b) non-Archimedean groups of diffeomorphisms Diff(M) representations associated with Poisson measures on configuration spaces $Γ_M$ contained in products of manifolds $M^{\bf N}$ are investigated. Here the cases of infinite-dimensional Banach manifold M (3) (a), non-Archimdean locally compact and non-locally compact Banach manifolds (3) (b) are investigated.

math.RT↗