Related papers: Semigroups versus evolution families in the Loewne…
We prove that evolution families on complex complete hyperbolic manifolds are in one to one correspondence with certain semicomplete non-autonomous holomorphic vector fields, providing the solution to a very general Loewner type…
We consider evolution in the unit disk in which the sample paths are represented by the trajectories of points evolving randomly under the generalized Loewner equation. The driving mechanism differs from the SLE evolution, but nevertheless…
One-parameter semigroups of holomorphic functions appear naturally in various applications of Complex Analysis, and in particular, in the theory of (temporally) homogeneous Markov processes. A suitable analogue of one-parameter semigroups…
In this paper we introduce a general version of the Loewner differential equation which allows us to present a new and unified treatment of both the radial equation introduced in 1923 by K. Loewner and the chordal equation introduced in…
Loewner Theory, based on dynamical viewpoint, is a powerful tool in Complex Analysis, which plays a crucial role in such important achievements as the proof of famous Bieberbach's conjecture and well-celebrated Schramm's Stochastic Loewner…
We establish the relation between the Wigner-Weisskopf theory for the description of an unstable system and the theory of coupling to an environment. According to the Wigner-Weisskopf general approach, even within the pole approximation…
We introduce a special class of real semiflows, which is used to define a general type of evolution semigroups, associated to not necessarily exponentially bounded evolution families. Giving spectral characterizations of the corresponding…
Under broad conditions, evolutions due to two different Hamiltonians are shown to lead at some moment to orthogonal states. For two spin-1/2 systems subject to precession by different magnetic fields the achievement of orthogonalization is…
In this paper, we define and study Loewner chains and evolution families on finitely multiply-connected domains in the complex plane. These chains and families consist of conformal mappings on parallel slit half-planes and have one and two…
We characterize (in almost all cases) the holomorphic self-maps of the unit disk that intertwine two given linear fractional self-maps of the disk. The proofs are based on iteration and a careful analysis of the Denjoy-Wolff points. In…
Using concepts of noncommutative probability we show that the Loewner's evolution equation can be viewed as providing a map from paths of measures to paths of probability measures. We show that the fixed point of the Loewner map is the…
We review some results on the logarithmic convexity for evolution equations, a well-known method in inverse and ill-posed problems. We start with the classical case of self-adjoint operators. Then, we analyze the case of analytic…
In this paper, we extend a result of Schwick concerning normality and sharing values in one complex variable for families of holomorphic curves taking values in $\mathbb{P}^n$. We consider wandering moving hyperplanes (i.e., depending on…
The class of evolving groups is defined and investigated, as well as their connections to examples in the field of Galois cohomology. Evolving groups are proved to be Sylow Tower groups in a rather strong sense. In addition, evolving groups…
We introduce the concept evolutionary semigroups on path spaces, generalizing the notion of transition semigroups to possibly non-Markovian stochastic processes. We study the basic properties of evolutionary semigroups and, in particular,…
In this paper we introduce a general version of the notion of Loewner chains which comes from the new and unified treatment, given in [arXiv:0807.1594], of the radial and chordal variant of the Loewner differential equation, which is of…
This paper is concerned with a scalar nonlinear convolution equation which appears naturally in the theory of traveling waves for monostable evolution models. First, we prove that each bounded positive solution of the convolution equation…
Let $S_{1}=\left\{F_t\right\}_{t\geq 0}$ and $S_{2}=\left\{G_t\right\}_{t\geq 0}$ be two continuous semigroups of holomorphic self-mappings of the unit disk $\Delta=\{z:|z|<1\}$ generated by $f$ and $g$, respectively. We present conditions…
We obtain slow dynamics for self-adjoint semigroups and unitary evolution groups. For semigroups, the slow dynamics is for orbits, and for the average return probability in the case of unitary evolution groups. We present an application to…
Let K be a field of characteristic 2 and G a nonabelian locally finite 2-group. Let V(KG) be the group of units with augmentation 1 in the group algebra KG. An explicit list of groups is given, and it is proved that all involutions in V(KG)…