Search results for "operators"
showing 10 items of 228 documents
SPECTRAL INVARIANCE FOR CERTAIN ALGEBRAS OF PSEUDODIFFERENTIAL OPERATORS
2001
We construct algebras of pseudodifferential operators on a continuous family groupoid G that are closed under holomorphic functional calculus, contain the algebra of all pseudodifferential operators of order 0 on G as a dense subalgebra, and reflect the smooth structure of the groupoid G, when G is smooth. As an application, we get a better understanding on the structure of inverses of elliptic pseudodifferential operators on classes of non-compact manifolds. For the construction of these algebras closed under holomorphic functional calculus, we develop three methods: one using two-sided semi-ideals, one using commutators, and one based on Schwartz spaces on the groupoid.
Contemporary Ergonomics and Business 2011: Proceedings of the 1st International Scientific-Practical Conference of the Latvian Ergonomics Society (7 …
2011
All published papers are peer-reviewed.
Padziļināts ieskats funkcionalanalīzes kursa dažos jēdzienos un uzdevumos
2021
Darbā aplūkoti atsevišķi funkcionālanalīzes uzdevumi un jēdzieni (skalārais reizinājums un tā īpašības, Košī nevienādība un tās vispārinājumi, operatora norma) ar mērķi kritiski salīdzināt dažādos avotos atrodamo informāciju un sniegt (studentiem) labāku izpratni par apskatāmajiem jēdzieniem un uzdevumiem.
On Fourier integral operators with Hölder-continuous phase
2018
We study continuity properties in Lebesgue spaces for a class of Fourier integral operators arising in the study of the Boltzmann equation. The phase has a H\"older-type singularity at the origin. We prove boundedness in $L^1$ with a precise loss of decay depending on the H\"older exponent, and we show by counterexamples that a loss occurs even in the case of smooth phases. The results can be seen as a quantitative version of the Beurling-Helson theorem for changes of variables with a H\"older singularity at the origin. The continuity in $L^2$ is studied as well by providing sufficient conditions and relevant counterexamples. The proofs rely on techniques from Time-frequency Analysis.
Compactness of Fourier integral operators on weighted modulation spaces
2019
Using the matrix representation of Fourier integral operators with respect to a Gabor frame, we study their compactness on weighted modulation spaces. As a consequence, we recover and improve some compactness results for pseudodifferential operators.
Closed injective ideals of multilinear operators, related measures and interpolation
2020
[EN] We introduce and discuss several ways of extending the inner measure arisen from the closed injective hull of an ideal of linear operators to the multilinear case. In particular, we consider new measures that allow to characterize the operators that belong to a closed injective ideal of multilinear operators as those having measure equal to zero. Some interpolation formulas for these measures, and consequently interpolation results involving ideals of multilinear operators, are established. Examples and applications related to summing multilinear operators are also shown.
A short note on Non-boson operators from a 1-dimensional gravitational like Hamiltonian
2012
In this paper, using factorization technique, we find the ground state for a 1--dimensional gravitational like Hamiltonian.
Instability of Equilibrium States for Coupled Heat Reservoirs at Different Temperatures
2007
Abstract We consider quantum systems consisting of a “small” system coupled to two reservoirs (called open systems). We show that such systems have no equilibrium states normal with respect to any state of the decoupled system in which the reservoirs are at different temperatures, provided that either the temperatures or the temperature difference divided by the product of the temperatures are not too small. Our proof involves an elaborate spectral analysis of a general class of generators of the dynamics of open quantum systems, including quantum Liouville operators (“positive temperature Hamiltonians”) which generate the dynamics of the systems under consideration.
Infinitely many solutions for a perturbed nonlinear Navier boundary value problem involving the -biharmonic
2012
By using critical point theory, we establish the existence of infinitely many weak solutions for a class of elliptic Navier boundary value problems depending on two parameters and involving the p-biharmonic operator. © 2012 Elsevier Ltd. All rights reserved.
Adiabatic Time-Dependent Hartree-Fock Calculations of the Optimal Path, the Potential, and the Mass Parameter for Large-Amplitude Collective Motion
1980
The adiabatic time-dependent Hartree-Fock theory is reformulated in order to yield a simple differential equation for the collective path with accompanying simple expressions for the collective mass and the potential. With use of three-dimensional coordinate- and momentum-space techniques and density-dependent interactions, the new adiabatic time-dependent Hartree-Fock formalism is applied to $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$ scattering and correspondingly to the fission mode of $^{8}\mathrm{Be}$. In the overlapping region the resulting collective mass deviates strongly from the reduced mass.