Many biological systems experience a periodic environment. Floquet theory is a mathematical tool to deal with such time periodic systems. It is not often applied in biology, because linkage between the mathematics and the biology is not available. To create this linkage, we derive the Floquet theory for natural systems. We construct a framework, where the rotation of the Earth is causing the pe...

there are many different ways to subdivide the spectrum of a bounded linear operator; some of them aremotivated by applications to physics (in particular, quantum mechanics). in this study, the relationship betweenthe subdivisions of spectrum which are not required to be disjoint and goldberg's classification are given.moreover, these subdivisions for some summability methods are studied.

a generalization of the known results in fusion frames and $g$-frames theory to continuous fusion frames which defined by m. h. faroughi and r. ahmadi, is presented in this study. continuous resolution of the identity (cri) is introduced, a new family of cri is constructed, and a number of reconstruction formulas are obtained. also, new results are given on the duality of continuous fusion fram...

Abstract Continuous frames and tensor products are important topics in theoretical physics. This paper combines those concepts. We derive fundamental properties of continuous for product Hilbert spaces. includes, example, the consistency property, i.e. preservation frame property under product, description canonical dual tensors by on space level. show full characterization all systems a given ...

We study invertibility and compactness of positive Toeplitz operators associated to a continuous Parseval frame on Hilbert space. As applications, we characterize affine Weyl-Heisenberg localization as well give uncertainty principles for the transforms.

Mathematical Morphology is a nonlinear image processing theory, which is currently based on complete lattices. This work extends its scope to complete semilattices, which are more general. Speci c morphological operators de ned in complete semilattices are shown, by means of simulations, to be potentially useful in some video processing applications, like detection of fast motion, extraction of...

In this work we will investigate how to find a matrix representation of operators on a Hilbert space H with Bessel sequences, frames and Riesz bases as an extension of the known method of matrix representation by ONBs. We will give basic definitions of the functions connecting infinite matrices defining bounded operators on l and operators onH. We will show some structural results and give some...

Electromagnetic and weak current operators for interacting systems should properly commute with the Poincaré generators and satisfy Hermiticity. The electromagnetic current should also satisfy P and T covariance and continuity equation. In front-form dynamics the current can be constructed from auxiliary operators, defined in a Breit frame where initial and final three-momenta of the system are...

Frames for Hilbert spaces are interesting mathematicians but also important applications in, e.g., signal analysis and physics. In both mathematics physics, it is natural to consider a full scale of spaces, not only single one. this paper, we study how certain frame-related properties sequence in one the such as completeness or property being (semi-) frame, propagate other ones spaces. We link ...

In this paper we deal with the connection of frames with the class of Hilbert Schmidt operators. First we give an easy criteria for operators being in this class using frames. It is the equivalent to the criteria using orthonormal bases. Then we construct Bessel sequences frames and Riesz bases for the class of Hilbert Schmidt operators using the tensor product of such sequences in the original...