On convergence of spectral expansions of Dirac operators with regular boundary conditions
Sign Up to like & getrecommendations! Published in 2022 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201900454
Abstract: Spectral problems for the Dirac operator with regular but not strongly regular boundary conditions and complex‐valued potential summable over a finite interval are considered. The purpose of this paper is to find conditions under which… read more here.
Keywords: convergence spectral; dirac operators; spectral expansions; expansions dirac ... See more keywords
On Weighted Dirac Operators and Their Fundamental Solutions for Anisotropic Media
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DOI: 10.1007/s00006-018-0860-0
Abstract: The heat transfer problem in isotropic media has been studied extensively in Clifford analysis, but very little in the anisotropic case for this setting. As a first step in this way, we introduce in this… read more here.
Keywords: fundamental solutions; dirac operators; solutions anisotropic; weighted dirac ... See more keywords
Fundamental Solution for Natural Powers of the Fractional Laplace and Dirac Operators in the Riemann–Liouville Sense
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DOI: 10.1007/s00006-019-1029-1
Abstract: In this paper, we study the fundamental solution of natural powers of the n-parameter fractional Laplace and Dirac operators defined via Riemann–Liouville fractional derivatives. To do this we use iteration through the fractional Poisson equation… read more here.
Keywords: laplace; natural powers; fractional laplace; dirac operators ... See more keywords
Partial Inverse Problems for Dirac Operators on Star Graphs
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DOI: 10.1007/s00009-020-01620-5
Abstract: Partial inverse problems for Dirac operators on star graphs are studied. We consider Dirac operators on the graphs, and prove that the potential on one edge is uniquely determined by part of its spectra and… read more here.
Keywords: dirac operators; problems dirac; star graphs; inverse problems ... See more keywords
Limiting Absorption Principle and Strichartz Estimates for Dirac Operators in Two and Higher Dimensions
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DOI: 10.1007/s00220-018-3231-8
Abstract: In this paper we consider Dirac operators in $${\mathbb{R}^n}$$Rn, $${n \ge 2}$$n≥2, with a potential V. Under mild decay and continuity assumptions on V and some spectral assumptions on the operator, we prove a limiting… read more here.
Keywords: dirac operators; limiting absorption; strichartz estimates; absorption principle ... See more keywords
Dynamical Localization for Discrete Anderson Dirac Operators
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DOI: 10.1007/s10955-017-1746-6
Abstract: We establish dynamical localization for random Dirac operators on the d-dimensional lattice, with $$d\in \left\{ 1, 2, 3\right\} $$d∈1,2,3, in the three usual regimes: large disorder, band edge and 1D. These operators are discrete versions… read more here.
Keywords: dirac operators; disorder; dirac; localization discrete ... See more keywords
Inverse resonance scattering for Dirac operators on the half-line
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DOI: 10.1007/s13324-020-00453-5
Abstract: We consider massless Dirac operators on the half-line with compactly supported potentials. We solve the inverse problems in terms of Jost function and scattering matrix (including characterization). We study resonances as zeros of Jost function… read more here.
Keywords: resonance; half line; dirac operators; operators half ... See more keywords
K-homology and Fredholm operators I: Dirac operators
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Geometry and Physics"
DOI: 10.1016/j.geomphys.2018.08.008
Abstract: This is an expository paper which gives a proof of the Atiyah-Singer index theorem for Dirac operators, presenting the theorem as a computation of the K-homology of a point. This paper and its follow up… read more here.
Keywords: index; dirac operators; homology fredholm; fredholm operators ... See more keywords
Dispersive estimates for massive Dirac operators in dimension two
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DOI: 10.1016/j.jde.2018.01.019
Abstract: Abstract We study the massive two dimensional Dirac operator with an electric potential. In particular, we show that the t − 1 decay rate holds in the L 1 → L ∞ setting if the… read more here.
Keywords: dispersive estimates; threshold energies; dirac operators; estimates massive ... See more keywords
Analysis of zero modes for Dirac operators with magnetic links
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DOI: 10.1016/j.jfa.2017.12.006
Abstract: In this paper we provide a means to approximate Dirac operators with magnetic fields supported on links in $\mathbb{S}^3$ (and $\mathbb{R}^3$) by Dirac operators with smooth magnetic fields. We then proceed to prove that under… read more here.
Keywords: magnetic fields; analysis; dirac operators; analysis zero ... See more keywords
Two-dimensional Dirac operators with singular interactions supported on closed curves
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DOI: 10.1016/j.jfa.2020.108700
Abstract: Abstract We study the two-dimensional Dirac operator with a class of interface conditions along a smooth closed curve, which model the so-called electrostatic and Lorentz scalar interactions of constant strengths, and we provide a rigorous… read more here.
Keywords: operators singular; singular interactions; dimensional dirac; dirac operators ... See more keywords