Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/spectral-properties-of-the-dirac-operator-on-the-real-line-z9IzA3ShXh
References (24)
-
(1953)
Pochti-periodicheskie funktsii (Almost Periodic Functions) -
G. Birkhoff (1908)
On the asymptotic character of the solutions of certain linear differential equations containing a parameterTransactions of the American Mathematical Society, 9
-
Анатолий Баскаков, Anatoly Baskakov, Дмитрий Поляков, Dmitry Polyakov (2017)
Метод подобных операторов в спектральном анализе оператора Хилла с негладким потенциалом@@@The metod of similar operators in spectral analysis for Hill operator with nonsmooth potentialMatematicheskii Sbornik, 208
-
P. Dirac (1928)
The quantum theory of the electronProceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences, 117
-
H. Reiter (1968)
Classical Harmonic Analysis and Locally Compact Groups -
P. Djakov, B. Mityagin (2010)
Unconditional convergence of spectral decompositions of 1D Dirac operators with regular boundary conditionsIndiana University Mathematics Journal, 61
-
P. Dirac (1928)
The Quantum Theory of the Electron. Part IIProceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences, 118
-
A. Savchuk (2018)
Dirac operator, eigen- and associated functions, conditional basis, Riesz basis.On the basis property of eigen and associated functions of 1D Dirac operatorIzvestiya: Mathematics, 82
-
M. Burlutskaya (2019)
Classical and Generalized Solutions of a Mixed Problem for a System of First-Order Equations with a Continuous PotentialComputational Mathematics and Mathematical Physics, 59
-
A. Baskakov, I. Krishtal, N. Uskova (2018)
Linear Differential Operator with an Involution as a Generator of an Operator GrouparXiv: Spectral Theory
-
L. Loomis (1953)
An Introduction to Abstract Harmonic Analysis -
A. Baskakov, I. Krishtal, N. Uskova (2020)
Closed operator functional calculus in Banach modules and applicationsJournal of Mathematical Analysis and Applications
-
A. Baskakov, Aleksey Derbushev, A. Shcherbakov (2011)
The method of similar operators in the spectral analysis of non-self-adjoint Dirac operators with non-smooth potentialsIzvestiya: Mathematics, 75
-
P. Djakov, B. Mityagin (2006)
Instability zones of periodic 1-dimensional Schrödinger and Dirac operatorsRussian Mathematical Surveys, 61
-
A. Baskakov, I. Krishtal (2011)
Memory estimation of inverse operatorsJournal of Functional Analysis, 267
-
(1965)
Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v gil’bertovom prostranstve (Introduction to the Theory of Linear Nonself-Adjoint Operators in a Hilbert Space) -
K. Engel, R. Nagel (1999)
One-parameter semigroups for linear evolution equationsSemigroup Forum, 63
-
J. Tamarkin (1928)
Some general problems of the theory of ordinary linear differential equations and expansion of an arbitrary function in series of fundamental functionsMathematische Zeitschrift, 27
-
A. Savchuk (2018)
On the basis property of the system of eigenfunctions and associated functions of a one-dimensional Dirac operatorIzvestiya: Mathematics, 82
-
A. Baskakov, I. Krishtal (2005)
Harmonic analysis of causal operators and their spectral propertiesIzvestiya: Mathematics, 69
-
G. Birkhoff (1908)
Boundary value and expansion problems of ordinary linear differential equationsTransactions of the American Mathematical Society, 9
-
A. Baskakov, I. Krishtal, N. Uskova (2018)
Similarity techniques in the spectral analysis of perturbed operator matricesJournal of Mathematical Analysis and Applications
-
A. Baskakov, D. Polyakov (2017)
The method of similar operators in the spectral analysis of the Hill operator with nonsmooth potentialSbornik: Mathematics, 208
-
A. Savchuk, A. Shkalikov (2014)
Dirac operator with complex-valued summable potentialMathematical Notes, 96
- Publisher
- Springer Journals
- Copyright
- Copyright © Pleiades Publishing, Ltd. 2021
- ISSN
- 0012-2661
- eISSN
- 1608-3083
- DOI
- 10.1134/S0012266121020026
- Publisher site
- See Article on Publisher Site
Abstract
We study the asymptotics of the spectrum of the Dirac operator on the real line with apotential in \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L_2$$\end{document}. It is shown that the spectrum of such an operatorlies in a domain of the complex plane symmetric about the real axis and bounded by the graph ofsome continuous real-valued square integrable function. To prove this, we use the\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L_1$$\end{document}-functional calculus for self-adjoint operators and asuitable similarity transformation.
Journal
Differential Equations – Springer Journals
Published: Mar 19, 2021