Slanted matrices, Banach frames, and sampling

In this paper we present a rare combination of abstract results on the spectral properties of slanted matrices and some of their very specific applications to frame theory and sampling problems. We show that for a large class of slanted matrices boundedness below of the corresponding operator in $\ell^p$ for some $p$ implies boundedness below in $\ell^p$ for all $p$. We use the established resultto enrich our understanding of Banach frames and obtain new results for irregular sampling problems. We also present a version of a non-commutative Wiener's lemma for slanted matrices

Novel mechanism for temperature-independent transitions in flexible molecules: role of thermodynamic fluctuations

Novel physical mechanism is proposed for explanation of temperature-independent transition reactions in molecular systems. The mechanism becomes effective in the case of conformation transitions between quasi-isoenergetic molecular states. It is shown that at room temperatures, stochastic broadening of molecular energy levels predominates the energy of low frequency vibrations accompanying the transition. This leads to a cancellation of temperature dependence in the stochastically averaged rate constants. As an example, physical interpretation of temperature-independent onset of P2X_3 receptor desensitization in neuronal membranes is provided.Comment: 4 pages, 1 figur

Harmonic analysis of causal operators and their spectral properties

The definition and study of causal operators are based on the representation theory of group algebras. We study the structure of the spectra of causal operators, obtain conditions for causal invertibility and state criteria for a causal operator to belong to the radical

Effective risk communication as a factor in managing protests attitudes in a local community

Contemporary research into the perception of environmental risks suffers from poor knowledge of risk communication in the local community and of how different ways of risk communication affect protest attitudes. This study aims to clarify communication strategies and practices used by members of local communities as a protest response to environmental threats. The work builds on the cultural theory developed by Douglas, Dake, Bremen, and others. This theory distinguishes between several cultural types (hierarchism, individualism, communitarianism, and egalitarianism), which differ in how environmental risks are perceived and what forms risk communication takes. The study investigates the case of the village of Nivenskoe in Russia’s Kaliningrad region where residents opposed the development of a potassium salt deposit. It is concluded that egalitarians and communitarians are more likely than hierarchists and individualists to participate in protests when a serious environmental threat arises. Respondents of all cultural types tend to trust information coming from their close social network, public figures, and environmentalists whereas people of business are trusted the least

Prony's Method in Banach Modules

We show that the classical Prony's method for recovery of a sparse signal from its consecutive Fourier coefficients can be viewed as a spectral identification problem for an unknown restriction of a known linear operator. This presents a unified point of view on various existing and novel generalizations and applications of the method, some of which are discussed in this paper

Method of similar operators in harmonious Banach spaces

We consider similarity transformations of a perturbed linear operator $A-B$ in a complex Banach space $\mathcal{X}$, where the unperturbed operator $A$ is a generator of a Banach $L_1(\mathbb{R})$-module and the perturbation operator $B$ is a bounded linear operator. The result of the transformation is a simpler operator $A-B_0$. For example, if $A$ is a differentiation operator and $B$ is an operator of multiplication by an operator-valued function, then $B_0$ is an operator of multiplication by a function that is a restriction of an entire function of exponential type and could be $0$ in some cases. As a consequence, we derive the spectral invariance of the operator $A-B$ in a large class of spaces. The study is based on a widely applicable modification of the method of similar operators that is also presented in the paper. This non-traditional modification is rooted in the spectral theory of Banach $L_1(\mathbb{R})$-modules