相关论文: Wave packet frames generated by hyponormal operato…

In this paper, we derive a new class of methods for the classic 2D phase unwrapping problem of recovering a phase function from its wrapped form. For this, we consider the wrapped phase as a wavefront aberration in an optical system, and…

Let $T:H_1\rightarrow H_2$ be a bounded linear operator defined between complex Hilbert spaces $H_1$ and $H_2$. We say $T$ to be \textit{minimum attaining} if there exists a unit vector $x\in H_1$ such that $\|Tx\|=m(T)$, where…

We show that the spin wavelets on the sphere $S^2$, which were constructed by the first author and Marinucci in an earlier article, can be chosen so as to form a nearly tight frame. These spin wavelets can be applied to the study of the…

With a densely defined symmetric semi-bounded operator of nonzero defect indexes $L_0$ in a separable Hilbert space ${\cal H}$ we associate a topological space $\Omega_{L_0}$ ({\it wave spectrum}) constructed from the reachable sets of a…

We study the microlocal properties of bisingular operators, a class of operators on the product of two compact manifolds. We define a wave front set for such operators, and analyse its properties. We compare our wave front set with the $SG$…

A method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random (possibly correlated) Jacobi matrix. As an application, one obtains sharp upper bounds…

We study the typical behavior of bounded linear operators on infinite dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies. In particular, we investigate typical spectral…

Weakly centered and spectrally weakly cenetered weighted composition operators in $L^2$-spaces are characterized. Criteria for existence of invariant subspaces are given. Additional results and examples are supplied.

It was shown in arXiv:0906.2527, that in finite-dimensional Hilbert spaces each operator system corresponds to some channel, for which this operator system will be an operator graph. This work is devoted to finding necessary and sufficient…

In this work, we investigate the dynamics of the wave packet traveling through a porous semiconductor channel, with the defects being simulated by a disordered scattering region produced by obstruction potentials. The theoretical framework…

We develop a computing framework that leverages wave propagation within an interconnected network, where nodes and edges possess wave manipulation capabilities, such as frequency mixing or time delay. This computing paradigm can not only…

This paper introduces and investigates the class of \textit{$k$-quasi $n$-power posinormal operators} in Hilbert spaces, generalizing both posinormal and $n$-power posinormal operators. We establish fundamental properties including matrix…

The phenomenon of wave packet diffraction in space and time is described. It consists in a diffraction pattern whose spatial location progresses with time. The pattern is produced by wave packet quantum scattering off an attractive or…

In this paper we have generalized and studied the $K$-Weyl-Heisenberg frames, where $K$ is a bounded linear operator on $L^2(\mathbb{R}^d)$. We have obtained necessary and sufficient conditions for acertain system to be a…

In this article we initiate the study of 1+ 2 dimensional wave maps on a curved spacetime in the low regularity setting. Our main result asserts that in this context the wave maps equation is locally well-posed at almost critical…

G\v avruta studied atomic systems in terms of frames for range of operators (that is, for subspaces), namely $K$-frames, where the lower frame condition is controlled by the Hilbert-adjoint of a bounded linear operator $K$. For a locally…

We prove the uniform hyperbolicity of the near-parabolic renormalization operators acting on an infinite-dimensional space of holomorphic transformations. This implies the universality of the scaling laws, conjectured by physicists in the…

A problem of a wave identification is formulated. An example is considered in conditions of one-dimensional Cauchy problem for conventional string equation in matrix form and its inhomogeneous two-component version. The acoustic and…

In this paper, some sub-classes of paranormal weighted conditional expectation type operators, such as *-paranormal, quasi-*-paranormal and (n; k)-quasi-*-paranormal weighted conditional expectation type opera- tors on $L^2(\Sigma)$ are…

In previous work, we have argued that measurement using a radar can be viewed as taking the expected value of an operator. The operator usually represents some aspect of the characteristics of the object being tracked (such as Doppler,…