相关论文: Infinitesimal generators of invertible evolution f…
The logarithmic representation of infinitesimal generators is generalized to the cases when the evolution operator is unbounded. The generalized result is applicable to the representation of infinitesimal generators of unbounded evolution…
Generally-unbounded infinitesimal generators are studied in the context of operator topology. Beginning with the definition of seminorm, the concept of locally convex topological vector space is introduced as well as the concept of…
The concept of logarithmic representation of infinitesimal generators is introduced, and it is applied to clarify the algebraic structure of bounded and unbounded infinitesimal generators. In particular, by means of the logarithmic…
The operator algebra is introduced based on the framework of logarithmic representation of infinitesimal generators. In conclusion a set of generally-unbounded infinitesimal generators is characterized as a module over the Banach algebra.
The relativistic formulation of abstract evolution equations is introduced. The corresponding logarithmic representation is shown to exist without assuming the invertible property of evolution operators. Consequently, by means of the…
Quadratic harnesses are time-inhomogeneous Markov polynomial processes with linear conditional expectations and quadratic conditional variances with respect to the past-future filtrations. Typically they are determined by five numerical…
We study the infinitesimal generators of evolutions of linear mappings on the space of polynomials, which correspond to a special class of Markov processes with polynomial regressions called quadratic harnesses. We relate the infinitesimal…
For a broad class of the Levy processes the new form (convolution type) of the infinitesimal generators is introduced. It leads to the new notions: a truncated generator, a quasi-potential. The probability of the Levy process remaining…
We extend the notions of finite free convolution and finite free cumulants to the setting of formal power series by introducing their natural analogues, namely $t$-deformed convolution and $t$-deformed cumulants. In this framework, we…
Operator representation of Cole-Hopf transform is obtained based on the logarithmic representation of infinitesimal generators. For this purpose the relativistic formulation of abstract evolution equation is introduced. Even independent of…
We characterize the infinitesimal generator of a semigroup of linear fractional self-maps of the unit ball in $\mathbb C^n$, $n\geq 1$. For the case $n=1$ we also completely describe the associated Koenigs function and we solve the…
Certain infinite families of operator identities related to powers of positive root generators of (super) Lie algebras of first-order differential operators and $q$-deformed algebras of first-order finite-difference operators are presented.
We consider linear bounded operators acting in Banach spaces with a basis, such operators can be represented by an infinite matrix. We prove that for an invertible operator there exists a sequence of invertible finite-dimensional operators…
Explicit generators are given for the ring of invariant polynomials under the coadjoint representation of certain inhomogeneous groups.
In this article we investigate the spectral properties of the infinitesimal generator of an infinite system of master equations arising in the analysis of the approach to equilibrium in statistical mechanics. The system under investigation…
We construct natural symbolic representations of intrinsically ergodic, but not necessarily expansive, principal algebraic actions of countably infinite amenable groups and use these representations to find explicit generating partitions…
The rotation group is formulated based on the abstract $B(X)$-module framework. Although the infinitesimal generators of rotation group include differential operators, the rotation group is formulated utilizing the framework of bounded…
This paper presents a novel approach to constructing finite generating sets for infinitely generated ideals. By integrating algebraic and computational techniques, we provide a method to identify finite generators, demonstrated through…
We introduce unbounded strongly irreducible operators and transitive operators. These operators are related to a certain class of indecomposable Hilbert representations of quivers on infinite-dimensional Hilbert spaces. We regard the theory…
In this paper, we study matricial representations of certain finitely presented groups with N-generators of order-2. As an application, we consider a group algebra under our representations. Specifically, we characterize the inverses of all…