Gamma-type operators and the Black–Scholes semigroup

We study Gamma-type operators from the analytic and probabilistic viewpoint in the setting of weighted continuous function spaces and estimate the rate of convergence of their iterates towards their limiting semigroup, providing, in this way, a quantitative version of the classical Trotter approximation theorem. The semigroup itself has some interest, since it is generated by the Black–Scholes operator, frequently occurring in the theory of option pricing in mathematical finance.     

Analyticity of the global attractor for damped forced periodic Korteweg–de Vries equation

We consider here a weakly damped forced periodic KdV equation. We prove that if the forcing term is analytic in space, then the global attractor is also contained into a space of analytic functions. This result was conjectured in [23].     

Analyticity of the Schr?dinger propagator on the Heisenberg group

We discuss the analytic extension property of the Schr?dinger propagator for the Heisenberg sublaplacian and some related operators. The result for the sublaplacian is proved by interpreting the sublaplacian as a direct integral of an one parameter family of dilated special Hermite operators.     

A presentation for the singular part of the full transformation semigroup

The (full) transformation semigroup T_n\mathcal{T}_{n} is the semigroup of all functions from the finite set {1,…,n} to itself, under the operation of composition. The symmetric group S_n í T_n{\mathcal{S}_{n}\subseteq \mathcal{T}_{n}} is the group of all permutations on {1,…,n} and is the group of units of T_n\mathcal{T}_{n}. The complement T_n\S_n\mathcal{T}_{n}\setminus \mathcal{S}_{n} is a subsemigroup (indeed an ideal) of T_n\mathcal{T}_{n}. In this article we give a presentation, in terms of generators and relations, for T_n\S_n\mathcal{T}_{n}\setminus \mathcal{S}_{n}, the so-called singular part of T_n\mathcal{T}_{n}.     

On the ergodic theorem in the Kozlov–Treshchev form for an operator semigroup

We study nonuniform ergodic averages of the Kozlov – Treshchev type for operator semigroups and obtain estimates for the corresponding maximal functions.     

Fiat categorification of the symmetric inverse semigroup $$\textit{IS}_n$$ and the semigroup $$F^*_n$$Fn∗

Starting from the symmetric group \(S_n\), we construct two fiat 2-categories. One of them can be viewed as the fiat “extension” of the natural 2-category associated with the symmetric inverse semigroup (considered as an ordered semigroup with respect to the natural order). This 2-category provides a fiat categorification for the integral semigroup algebra of the symmetric inverse semigroup. The other 2-category can be viewed as the fiat “extension” of the 2-category associated with the maximal factorizable subsemigroup of the dual symmetric inverse semigroup (again, considered as an ordered semigroup with respect to the natural order). This 2-category provides a fiat categorification for the integral semigroup algebra of the maximal factorizable subsemigroup of the dual symmetric inverse semigroup.     

Analog of the Löwner–Kufarev equation for the semigroup of conformal mappings of the disk into itself with fixed points and invariant diameter

Mathematical Notes -     

On non–symmetric generalized schrodinger semigroup

In this paper some general phenomena are described for not necessarily systemeric so–called generalized Schrödinger semigroups (or generalized absorption/exciatation semigroups). These results are also applicable in case we consider Schrödinger semigroups on R ^v. In particular we describe some results on integral kernels: continuity, pointwise inequalities, ultracontractivity etc.For these inequalities we use a kind of stochastic bridge measure. The operator H is a closed linear extension of the operator H ⁰ + V in the space C ⁰(E) Here E is a locally compact second countable Hausdorff space and –H ₀ is supposed to generate a Feller semigroup in C ₀(E). Results in L^p (E,m) are also availale. Some examples are given     

Nonpresentability of the semigroup ω ω over ℍmathbb{F}(ℝ)

We prove that the semigroup of all functions from the set of natural numbers to natural numbers by composition has no one-valued Σ-presentations with parameters over the hereditarily finite superstructure over the real numbers.     

A note on the approximate amenability of semigroup algebras

It is known that the bicyclic semigroup S ₁ is an amenable inverse semigroup. In this note we show that the convolution semigroup algebra ℓ ¹(S ₁) is not approximately amenable.     

A Generalization of C—semigroup

§ 1.ＴｈｅＧｅｎｅｒａｌＣ ｓｅｍｉｇｒｏｕｐ　Ｉｎｔｈｉｓｐａｐｅｒ,ｗｅｌｅｔＸｂｅａＢａｎａｃｈｓｐａｃｅ,ａｎｄＢ(Ｘ)ｔｈｅｓｐａｃｅｏｆａｌｌｂｏｕｎｄｅｄｌｉｎｅａｒｏｐｅｒａｔｏｒｓｆｒｏｍＸｉｎｔｏＸ .　Ｄｅｆｉｎｉｔｉｏｎ 1 .1　ＳｕｐｐｏｓｅＣｉｓａｂｏｕｎｄｅｄｉｎｊｅｃｔｉｖｅｏｐｅｒａｔｏｒｆｒｏｍＸｉｎｔｏＸ .Ｔｈｅｆａｍｉｌｙｏｆｂｏｕｎｄｅｄｌｉｎｅａｒｏｐｅｒａｔｏｒｓ (Ｓ(ｔ) ) ｔ≥ 0 ｉｓａｇｅｎｅｒａｌＣ ｓｅｍｉｇｒｏｕｐｉｆｉｔｈａｓｔｈｅｆｏｌｌｏｗｉｎｇ…     

A proof of Devadze’s theorem on generators of the semigroup of Boolean matrices

In 1968 Devadze described, without a proof, minimal sets of generators of the semigroup of n×n Boolean matrices. We provide a proof of Devadze’s theorem.     

A Cox Process Involved in the Bose–Einstein Condensation

The point process corresponding to the configurations of bosons in standard conditions is a Cox process driven by the square norm of a centered Gaussian process. This point process is infinitely divisible. We point out the fact that this property is preserved by the Bose–Einstein condensation phenomenon and show that the obtained point process after such a condensation occured, is still a Cox process but driven by the square norm of a shifted Gaussian process, the shift depending on the density of the particles. This law provides an illustration of a “super”- Isomorphism Theorem existing above the usual Isomorphism Theorem of Dynkin available for Gaussian processes. Submitted: February 8, 2008. Accepted: March 5, 2008.