arXiv subjects
Publications and source records attributed to Stevan Pilipovi\' c.
In this paper, we continue our previous research studies of exponential ultradistribution semigroups in Banach spaces. The existence and uniqueness of analytical solutions of abstract fractional relaxation equations associated with the generators of exponential ultradistribution semigroups have been considered. Some other results are also proved.
We analyze $f$-frequently hypercyclic, $q$-frequently hypercyclic ($q> 1$) and frequently hypercyclic $C_{0}$-semigroups ($q=1$) defined on complex sectors, working in the setting of separable infinite-dimensional Fréchet spaces. Some structural results of ours are given for a general class of ${\mathcal F}$-frequently hypercyclic $C_{0}$-semigroups, as well. We investigate generalized frequently hypercyclic translation semigroups and generalized frequently hypercyclic semigroups induced by semiflows on weighted function spaces. Several illustrative examples are presented.
The main purpose of this paper is to investigate degenerate $C$-(ultra)distribution cosine functions in the setting of barreled sequentially complete locally convex spaces. In our approach, the infinitesimal generator of a degenerate $C$-(ultra)distribution cosine function is a multivalued linear operator and the regularizing operator $C$ is not necessarily injective. We provide a few important theoretical novelties, considering also exponential subclasses of degenerate $C$-(ultra)distribution cosine functions.
Our main goal in this paper is to investigate the (q-)exponential $C$-distribution semigroups and (q-)exponential $C$-ultradistribution semigroups in the setting of sequentially complete locally convex spaces. We contribute to previous work and the work of many other authors, providing additionally plenty of various examples and applications of obtained results.
The main purpose of this paper is to investigate $C$-distribution semigroups and $C$-ultradistribution semigroups in the setting of sequentially complete locally convex spaces. There are a few important theoretical novelties in this field and there are given some interesting examples.
Results of Da Prato and Sinestrari, on differential operators with non-dense domain but satisfying the Hille--Yosida condition, are applied in the setting of Beurling weighted spaces of ultradistributions $\DD'^{(s)}_{L^p}((0,T)\times U)$, where $U$ is open and bounded set in $\mathbb R^d$.