Related papers: Construction of dynamical semigroups by a function…
Differential regularization is applied to a field theory of a non-relativistic charged boson field $\phi$ with $\lambda (\phi {}^{*} \phi)^2$ self-interaction and coupling to a statistics-changing $U(1)$ Chern-Simons gauge field.…
A semi-analytic method to compute the first coefficients of the renormalization group functions on a random lattice is introduced. It is used to show that the two-dimensional $O(N)$ non-linear $\sigma$-model regularized on a random lattice…
In this paper, we introduce formulations of the Trotter Kato theorem for approximation of bi continuous semigroups that provide a useful framework whenever convergence of numerical approximations to solutions of PDEs are studied with…
Quantum Groups can be constructed by applying the quantization by deformation procedure to Lie groups endowed with a suitable Poisson bracket. Here we try to develop an understanding of these structures by investigating dynamical systems…
It is shown how to construct *-homomorphic quantum stochastic Feller cocycles for certain unbounded generators, and so obtain dilations of strongly continuous quantum dynamical semigroups on C* algebras; this generalises the construction of…
A quasi-automatic semigroup is defined by a finite set of generators, a rational (regular) set of representatives, such that if a is a generator or neutral, then the graph of right multiplication by a on the set of representatives is a…
A new class of fractional-order stochastic evolution equations of the form $(\partial_t + A)^\gamma X(t) = \dot{W}^Q(t)$, $t\in[0,T]$, $\gamma \in (0,\infty)$, is introduced, where $-A$ generates a $C_0$-semigroup on a separable Hilbert…
We solve the Kato square root problem for bounded measurable perturbations of subelliptic operators on connected Lie groups. The subelliptic operators are divergence form operators with complex bounded coefficients, which may have lower…
It is well known that the normaliser of a parabolic subgroup of a finite Coxeter group is the semidirect product of the parabolic subgroup by the stabiliser of a set of simple roots. We show that a similar result holds for all finite…
We give an Ito type formula for a semi group whose generarator is a positive pseudo-differential operator which does not in general satisfies maximumu principle.
Let $X_n = \{1,2,\dots,n\}$ be a finite set $(n\geq 2)$ and $T_n$ the full transformation semigroup on $X_n$. For a positive integer $l\leq n-1$, we define $$T_n(l) = \{\alpha\in T_n \colon \forall x,y\in X_n,\, |x-y| = l \;\Rightarrow\;…
We construct a new bounded functional calculus for the generators of bounded semigroups on Hilbert spaces and generators of bounded holomorphic semigroups on Banach spaces. The calculus is a natural (and strict) extension of the classical…
The non-perturbative functional renormalization group equation depends on the choice of a regulator function, whose main properties are a "coarse-graining scale" $k$ and an overall dimensionless amplitude $a$. In this paper we shall discuss…
A recent characterisation of Fock-adapted contraction operator stochastic cocycles on a Hilbert space, in terms of their associated semigroups, yields a general principle for the construction of such cocycles by approximation of their…
We give a short new proof of the Arendt-Chernoff-Kato theorem, which characterizes generators of positive C0 semigroups in order unit spaces. The proof avoids half-norms and subdifferentials, and is based on a sufficient condition for an…
This paper is to study some conditions on semigroups, generated by some class of non-densely defined operators in the closure of its domain, in order that certain bounded perturbations preserve some regularity properties of the semigroup…
We present a generation theorem for positive semigroups on an $L^1$ space. It provides sufficient conditions for the existence of positive and integrable solutions of initial-boundary value problems. An application to a two-phase cell cycle…
We study dynamical semigroups of positive, but not completely positive maps on finite-dimensional bipartite systems and analyze properties of their generators in relation to non-decomposability and bound-entanglement. An example of…
We derive a uniform bound for the difference of two contractive semigroups, if the difference of their generators is form-bounded by the Hermitian parts of the generators themselves. We construct a semigroup dynamics for second order…
The structure of the commutator algebra for conformal quantum mechanics is considered. Specifically, it is shown that the emergence of a dimensional scale by renormalization implies the existence of an anomaly or quantum-mechanical symmetry…