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We study band-dominated operators on (subspaces of) $L_p$-spaces over metric measure spaces of bounded geometry satisfying an additional property. We single out core assumptions to obtain, in an abstract setting, definitions of limit…
We consider the problem of the boundedness of maximal operators on BMO on shapes in $\mathbb{R}^n$. We prove that for bases of shapes with an engulfing property, the corresponding maximal function is bounded from BMO to BLO, generalising a…
We first consider two types of localizations of singular integral operators of convolution type, and show, under mild decay and smoothness conditions on the auxiliary functions, that their boundedness on the local Hardy space…
Metrics and pseudometrics are defined on the group of unitary operators in a Hilbert space. Several explicit formulas are derived. A special feature of the work is investigation of pseudometrics in unitary groups. The rich classes of…
In this article, the authors introduce Besov and Triebel-Lizorkin spaces on spaces of homogeneous type in the sense of Coifman and Weiss, prove that these (in)homogeneous Besov and Triebel-Lizorkin spaces are independent of the choices of…
We construct a generalized dynamics for particles moving in a symmetric space-time, i.e. a space-time admitting one or more Killing vectors. The generalization implies that the effective mass of particles becomes dynamical. We apply this…
The nonlinear geometry of operator spaces has recently started to be investigated. Many notions of nonlinear embeddability have been introduced so far, but, as noticed before by other authors, it was not clear whether they could be…
We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of…
Open discrete mappings with a modulus condition in metric spaces are considered. Some results related to local behavior of mappings as well as theorems about continuous extension to a boundary are proved.
A strong inhomogeneous static electric field is used to spatially disperse a supersonic beam of polar molecules, according to their quantum state. We show that the molecules residing in the lowest-lying rotational states can be selected and…
Living systems are capable of locomotion, reconfiguration, and replication. To perform these tasks, cells spatiotemporally coordinate the interactions of force-generating, "active" molecules that create and manipulate non-equilibrium…
Due to their rich level structure, molecules are well-suited for probing time variation of fundamental constants, precisely measuring parity violation and time-reversal non-invariance effects, studying quantum mechanical aspects of chemical…
We introduce a new scheme for controlling the sense of molecular rotation. By varying the polarization and the delay between two ultrashort laser pulses, we induce unidirectional molecular rotation, thereby forcing the molecules to rotate…
Observables and instruments have played significant roles in recent studies on the foundations of quantum mechanics. Sequential products of effects and conditioned observables have also been introduced. After an introduction in Section~1,…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…
In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum…
The understanding of molecular structure and function is at the very heart of the chemical and molecular sciences. Experiments that allow for the creation of structurally pure samples and the investigation of their molecular dynamics and…
This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded…