We introduce the notion of uniform γ –radonification of a family of operators, which unifies the notions of R–boundedness of a family of operators and γ –radonification of an individual operator. We study the properties of uniformly γ –radonifying families of operators in detail and apply our results to the stochastic abstract Cauchy problem dU(t) = AU(t)dt +BdW (t), U(0) = 0. Here, A is the ge...

It is due to the modularity of the analysis that results for cascaded systems have proved their utility in numerous control applications as well as in the development of general control techniques based on “adding integrators”. Nevertheless, the standing assumptions in most of the present literature on cascaded systems is that, when decoupled, the subsystems constituting the cascade are uniform...

We study Vector Addition Systems with States (VASS) extended in such a way that one of the manipulated integer variables can be tested to zero. For this class of system, it has been proved that the reachability problem is decidable. We prove here that boundedness, termination and reversal-boundedness are decidable for VASS with one zero-test. To decide reversal-boundedness, we provide an origin...

We study Vector Addition Systems with States (VASS) extended in such a way that one of the manipulated integer variables can be tested to zero. For this class of system, it has been proved that the reachability problem is decidable. We prove here that boundedness, termination and reversal-boundedness are decidable for VASS with one zero-test. To decide reversal-boundedness, we provide an origin...

In this paper we study the boundedness properties of certain oscillatory integrals with polynomial phase. We obtain sharp estimates for these oscillatory integrals. By the virtue of these estimates and extrapolation we obtain L boundedness for these oscillatory integrals under rather weak size conditions on the kernel function. Keywords—Fourier transform, oscillatory integrals, Orlicz spaces, B...

Wemake the first attempt to discuss stability and boundedness of solutions to stochastic Volterra integrodifferential equations with infinite delay (IDSVIDEs). By the Lyapunov-Krasovskii functional approach, we get kinds of sufficient criteria for stability and boundedness of solutions to IDSVIDEs. The main innovation here is that stochastic systems with infinite delay can retain stability and ...