Article
Mathematics
Jean-Pierre Antoine, Camillo Trapani
Summary: In this article, we examine the spectral behavior of a self-adjoint operator A in a Hilbert space H when it is expressed in terms of generalized eigenvectors. By utilizing the formalism of Gel'fand distribution bases, we investigate the conditions for the generalized eigenspaces to be one-dimensional, indicating a simple spectrum for A.
Article
Mathematics
Osmin Ferrer, Arley Sierra, Osvaldo Polo
Summary: This paper introduces the concept and properties of orthogonal frames in Krein spaces. It proves the independence of the choice of the fundamental symmetry and derives interesting properties from it. Additionally, it demonstrates the equivalence between orthogonal frames in a Krein space and orthogonal frames in its associated Hilbert space. The paper also characterizes dual frames to a given frame, which is a useful tool for constructing examples.
Article
Mathematics
S. K. Sharma, Nitin Sharma, Khole Timothy Poumai
Summary: This paper introduces and studies woven frames in quaternionic Hilbert spaces, giving properties and conditions on family of frames. Also, it presents a characterization of weaving frames in terms of a surjective-bounded right linear operator.
JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics
Osmin Ferrer, Arley Sierra, Jose Sanabria
Summary: This paper introduces the concept of discrete frames on soft Hilbert spaces using soft linear operators, extending the classical notion of frames on Hilbert spaces to algebraic structures on soft sets. The results demonstrate properties of frame operators and prove the frame decomposition theorem for every element in a soft Hilbert space. This theoretical framework has potential applications in signal processing, specifically in modeling data packets for communication networks.
Article
Mathematics
Guoqing Hong, Pengtong Li
Summary: This paper introduces and studies operator valued frames on quaternionic Hilbert spaces. A parametrization of Parseval operator valued frames is obtained using a class of partial isometries in the quaternionic Hilbert spaces. Many properties of vector frames on quaternionic Hilbert spaces are extended to operator valued frames. Moreover, the paper shows that all the operator valued frames can be obtained from a single operator valued frame. Finally, several results regarding duality and similarity of operator valued frames on quaternionic Hilbert spaces are presented.
Article
Physics, Multidisciplinary
Davide Lonigro
Summary: In this study, we investigate the phenomena of bound states and resonances in a system composed of two-level systems interacting with a one-dimensional boson field. We evaluate the self-energy of the model and provide an analytic expression that is applicable to a wide range of dispersion relations and coupling functions. Specifically, we analyze the case of identical two-level systems, distinguishing between dominant and suppressed contributions to the self-energy, and examine the phenomenology of bound states in the presence of a single dominant contribution.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Optics
Philip Caesar Flores, Eric A. Galapon
Summary: This paper studies the relativistic version of the Aharonov-Bohm time-of-arrival operator for spin-0 particles, and provides insights beyond the original results by taking its rigged Hilbert space extension. Time-of-arrival distributions are constructed using eigenfunctions that exhibit unitary arrival, and the expectation value is calculated, showing that particles can arrive earlier or later than expected classically. The constructed time-of-arrival distribution and expectation value are also consistent with special relativity.
Article
Mathematics
Deepshikha, Aniruddha Samanta
Summary: This paper explores the properties of weaving generalized frames and weaving generalized orthonormal bases, including their interrelation and optimal bounds. It also presents a characterization of weaving g-frames and illustrates the differences between weaving generalized Riesz bases and weaving Riesz bases.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2022)
Article
Mathematics, Applied
Ahmad Ahmadi
Summary: This paper focuses on the concepts of Riesz bases and pair of dual frames in the tensor product of Hilbert spaces, discussing special properties of pair of dual frames in these spaces. It demonstrates that Riesz bases and pair of dual frames in H circle times K are preserved under invertible and unitary operators on H, and presents a representation for Hilbert-Schmidt operators using a pair of dual frames.
RICERCHE DI MATEMATICA
(2021)
Article
Physics, Multidisciplinary
Dean Alvin L. Pablico, Eric A. Galapon
Summary: In this paper, we provide a complete description of a time of arrival (TOA) operator, which is conjugate with the system Hamiltonian, by explicitly solving all the terms in the expansion. We interpret the terms beyond the leading term as quantum corrections to the Weyl quantization of the classical arrival time, expressed as integrals of the interaction potential. We investigate the properties of these quantum corrections in detail and find that they always vanish for linear systems but are nonvanishing for nonlinear systems. Finally, we consider the example of an anharmonic oscillator potential.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Mathematics, Applied
Yuxiang Xu, Jinsong Leng
Summary: In this paper, new inequalities and Parseval identities for weaving frames in Hilbert spaces involving scalar lambda are established, with special cases obtained by suitable choices of lambda. These results generalize and improve on previous findings by Balan et al. and Gavruta.
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2021)
Article
Computer Science, Software Engineering
Amir Khosravi, Mohammad Reza Farmani
Summary: This paper investigates the characteristics and stability of piecewise scalable frames, and establishes a relationship between them and tensor product.
INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING
(2023)
Article
Mathematics
Fahimeh Arabyani-Neyshaburi, Ali Akbar Arefijamaal
Summary: This paper surveys the topic of weaving Hilbert space frames from the perspective of the duality principle, obtaining new properties and approaches for manufacturing pairs of woven frames. The study provides sufficient conditions under which a frame with its canonical dual, alternate duals, or approximate duals constitute concrete pairs of woven frames, and presents methods for constructing weaving frames using small perturbations. The findings demonstrate that the canonical duals of two woven frames are also woven.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2021)
Article
Mathematics, Applied
K. P. Isaev, R. S. Yulmukhametov
Summary: We describe some radial Fock type spaces that have Riesz bases of normalized reproducing kernels for certain entire functions. The spaces are characterized by radial subharmonic functions, and we prove the existence of Riesz bases under certain conditions.
ANALYSIS AND MATHEMATICAL PHYSICS
(2022)
Article
Mathematics
Dongwei Li, Jing Jiang, Yuxiang Xu
Summary: This paper investigates some new properties of weaving frames and provides conditions for a family of frames to be woven in Hilbert spaces. Characterizations of weaving frames in terms of operators are discussed. Additionally, a condition associated with the synthesis operators of frames is introduced to determine if the sequence of frames is woven. Finally, the paper proves the stability of a family of woven frames under invertible operators and small perturbations.
OPERATORS AND MATRICES
(2023)
