Zobrazeno 1 - 10
of 41
pro vyhledávání: '"Ibrogimov, Orif O."'
We derive quantitative bounds for eigenvalues of complex perturbations of the indefinite Laplacian on the real line. Our results substantially improve existing results even for real-valued potentials. For $L^1$-potentials, we obtain optimal spectral
Externí odkaz:
http://arxiv.org/abs/2004.10471
Publikováno v:
Annales Henri Poincar\'e 21, 2193-2217 (2020)
We provide quantitative estimates on the location of eigenvalues of one-dimensional discrete Dirac operators with complex $\ell^p$-potentials for $1\leq p\leq\infty$. As a corollary, subsets of the essential spectrum free of embedded eigenvalues are
Externí odkaz:
http://arxiv.org/abs/1910.10710
We study location of eigenvalues of one-dimensional discrete Schr\"odinger operators with complex $\ell^{p}$-potentials for $1\leq p\leq \infty$. In the case of $\ell^{1}$-potentials, the derived bound is shown to be optimal. For $p>1$, two different
Externí odkaz:
http://arxiv.org/abs/1903.08620
Publikováno v:
Math. Nachr. 294 (2021) 1333-1349
We derive sharp quantitative bounds for eigenvalues of biharmonic operators perturbed by complex-valued potentials in dimensions one, two and three.
Externí odkaz:
http://arxiv.org/abs/1903.01810
Autor:
Ibrogimov, Orif O.
Under minimal regularity conditions on the photon dispersion and the coupling function, we prove that the spin-boson model with two massless photons in $\mathbb{R}^d$ cannot have more than two bound state energies whenever the coupling strength is su
Externí odkaz:
http://arxiv.org/abs/1902.05549
Autor:
Ibrogimov, Orif O.
We study the spectrum of the spin-boson Hamiltonian with two bosons for arbitrary coupling $\alpha>0$ in the case when the dispersion relation of the free field is a bounded function. We derive an explicit description of the essential spectrum which
Externí odkaz:
http://arxiv.org/abs/1901.11534
Autor:
Ibrogimov, Orif O.
Publikováno v:
Annales Henri Poincare, 19(11):3561-3579, 2018
We study the spectrum of the spin-boson model with two photons in $\mathbb{R}^d$ for arbitrary coupling $\alpha>0$. It is shown that the discrete spectrum is finite and the essential spectrum consists of a half-line the bottom of which is a unique ze
Externí odkaz:
http://arxiv.org/abs/1801.06908
Publikováno v:
J. Pseudo-Differ. Oper. Appl. (2017) 8:147--166
Inspired by a result of Wong (Commun. Partial Differ. Equ. 13(10):1209-1221, 1988), we establish an analytic description of the essential spectrum of non-self-adjoint mixed-order systems of pseudo-differential operators on $L^2(\mathbb{R}^N) \oplus L
Externí odkaz:
http://arxiv.org/abs/1703.06344
Publikováno v:
Operator Theory: Advances and Applications 263 (2018), 321-334
We study the spectrum of an operator matrix arising in the spectral analysis of the energy operator of the spin-boson model of radioactive decay with two bosons on the torus. An analytic description of the essential spectrum is established. Further,
Externí odkaz:
http://arxiv.org/abs/1612.05459
Autor:
Ibrogimov, Orif O.
Publikováno v:
J. Math. Anal. Appl. 451 (2017) 473-496
The purpose of this paper is to study the essential spectrum of non-self-adjoint singular matrix differential operators in the Hilbert space $L^2(\mathbb{R})\oplus L^2(\mathbb{R})$ induced by matrix differential expressions of the form \begin{align}\
Externí odkaz:
http://arxiv.org/abs/1612.05193