Critical points of discrete periodic operators

被引：1

作者：

Faust, Matthew ^{[1
]}

Sottile, Frank ^{[1
]}

机构：

[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

来源：

JOURNAL OF SPECTRAL THEORY | 2024年 / 14卷 / 01期

关键词：

Bloch variety; Schr & ouml; dinger operator; Kushnirenko Theorem; Toric variety; Newton polytope;

D O I：

10.4171/JST/503

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the spectra of operators on periodic graphs using methods from combinatorial algebraic geometry. Our main result is a bound on the number of complex critical points of the Bloch variety, together with an effective criterion for when this bound is attained. We show that this criterion holds for Z 2 - and Z 3 -periodic graphs with sufficiently many edges and use our results to establish the spectral edges conjecture for some Z 2 -periodic graphs.

引用

页码：1 / 35

页数：35

共 50 条

[11] Fermi isospectrality for discrete periodic Schrodinger operators
Liu, Wencai
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2024, 77 (02) : 1126 - 1146
[12] Discrete eigenvalues of periodic operators with distant perturbations
Golovina A.M.
Journal of Mathematical Sciences, 2013, 189 (3) : 342 - 364
[13] Magnetic Schrodinger operators on periodic discrete graphs
Korotyaev, Evgeny
Saburova, Natalia
JOURNAL OF FUNCTIONAL ANALYSIS, 2017, 272 (04) : 1625 - 1660
[14] Discrete differential operators for periodic and two-periodic time functions
Sobczyk, Tadeusz
Radzik, Michal
Radwan-Praglowska, Natalia
COMPEL-THE INTERNATIONAL JOURNAL FOR COMPUTATION AND MATHEMATICS IN ELECTRICAL AND ELECTRONIC ENGINEERING, 2019, 38 (01) : 325 - 347
[15] Instability of singular critical points of definitizable operators
Langer, H
Najman, B
INTEGRAL EQUATIONS AND OPERATOR THEORY, 1997, 28 (01) : 60 - 71
[16] On the fixed points of monotonic operators in the critical case
Engibaryan, N. B.
IZVESTIYA MATHEMATICS, 2006, 70 (05) : 931 - 947
[17] PROPERTIES OF CRITICAL-POINTS AND OPERATORS IN ECONOMICS
CHICHILNISKY, G
KALMAN, PJ
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1977, 57 (02) : 340 - 349
[18] Instability of singular critical points of definitizable operators
H. Langer
B. Najman
Integral Equations and Operator Theory, 1997, 28 : 60 - 71
[19] ON BIFURCATION OF NOETHER POINTS IN DISCRETE SPECTRUM OF LINEAR OPERATORS
Rakhimov, D. G.
EURASIAN MATHEMATICAL JOURNAL, 2015, 6 (02): : 75 - 81
[20] Invariant Varieties of Periodic Points for the Discrete Euler Top
Saito, Satoru
Saitoh, Noriko
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2006, 2

← 1 2 3 4 5 →