{"results":[{"id":"arxiv_2503.08758","title":"Finite and full scale localization for the multi-frequency quasi-periodic CMV matrices","authors":[{"name":"Bei Zhang"},{"name":"Daxiong Piao"}],"abstract":"This paper formulates the finite and full-scale localization for multi-frequency quasi-periodic CMV matrices. This can be viewed as the CMV counterpart to the localization results by Goldstein, Schlag, and Voda [arXiv:1610.00380 (math.SP], Invent. Math. 217 (2019)) on multi-frequency quasi-periodic Schrödinger operators.","source":"arXiv","year":2025,"language":"en","subjects":["math.SP"],"url":"https://arxiv.org/abs/2503.08758","pdf_url":"https://arxiv.org/pdf/2503.08758","is_open_access":true,"published_at":"2025-02-22T01:24:02Z","score":69},{"id":"arxiv_2403.13620","title":"Upper bound for Steklov eigenvalues of warped products with fiber of dimension 2","authors":[{"name":"Jade Brisson"},{"name":"Bruno Colbois"}],"abstract":"In this note, we investigate the Steklov spectrum of the warped product $[0,L]\\times_h Σ$ equipped with the metric $dt^2+h(t)^2g_Σ$, where $Σ$ is a compact surface. We find sharp upper bounds for the Steklov eigenvalues in terms of the eigenvalues of the Laplacian on $Σ$. We apply our method to the case of metric of revolution on the 3-dimensional ball and we obtain a sharp estimate on the spectral gap between two consecutive Steklov eigenvalues.","source":"arXiv","year":2024,"language":"en","subjects":["math.SP","math.DG"],"url":"https://arxiv.org/abs/2403.13620","pdf_url":"https://arxiv.org/pdf/2403.13620","is_open_access":true,"published_at":"2024-03-20T14:13:46Z","score":68},{"id":"ss_f98165234399c724dc175aff8a1888a1237e3015","title":"On the Sum of Negative Eigenvalues of the Three-Dimensional Schrödinger Operator","authors":[{"name":"A. R. Aliev"},{"name":"E. H. Eyvazov"}],"abstract":"","source":"Semantic Scholar","year":2024,"language":"en","subjects":null,"doi":"10.1134/S0001434624010139","url":"https://www.semanticscholar.org/paper/f98165234399c724dc175aff8a1888a1237e3015","is_open_access":true,"published_at":"","score":68},{"id":"ss_d8eb23c47b5b809e112291b09e0079a8d5687fcd","title":"Global and Local Bounds on the Fundamental Ratio of Triangles and Quadrilaterals","authors":[{"name":"R. Arbon"}],"abstract":"We present a new, computer-assisted, proof that for all triangles in the plane, the equilateral triangle uniquely maximizes the ratio of the first two Dirichlet-Laplacian eigenvalues. This proves an independent proof the triangular Ashbaugh-Benguria-Payne-Polya-Weinberger conjecture first proved in arXiv:0707.3631 [math.SP] and arXiv:2009.00927 [math.SP]. Inspired by arXiv:1109.4117 [math.SP], the primary method is to use a perturbative estimate to determine a local optimum, and to then use a continuity estimate for the fundamental ratio to perform a rigorous computational search of parameter space. We repeat a portion of this proof to show that the square is a strict local optimizer of the fundamental ratio among quadrilaterals in the plane","source":"Semantic Scholar","year":2022,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/d8eb23c47b5b809e112291b09e0079a8d5687fcd","is_open_access":true,"citations":2,"published_at":"","score":66.06},{"id":"crossref_10.1007/s00208-017-1623-2","title":"A local converse theorem for $${\\mathrm {Sp}}_{2r}$$ Sp 2 r","authors":[{"name":"Qing Zhang"}],"abstract":"","source":"CrossRef","year":2017,"language":"en","subjects":null,"doi":"10.1007/s00208-017-1623-2","url":"https://doi.org/10.1007/s00208-017-1623-2","pdf_url":"http://link.springer.com/content/pdf/10.1007/s00208-017-1623-2.pdf","is_open_access":true,"citations":10,"published_at":"","score":61.3},{"id":"arxiv_1608.04825","title":"Spectral Theory Sum Rules, Meromorphic Herglotz Functions and Large Deviations","authors":[{"name":"Barry Simon"}],"abstract":"Short blurb for invited talk at AMS annual meeting in Atlanta; will appear in January AMS Notices","source":"arXiv","year":2016,"language":"en","subjects":["math.SP"],"url":"https://arxiv.org/abs/1608.04825","pdf_url":"https://arxiv.org/pdf/1608.04825","is_open_access":true,"published_at":"2016-08-17T01:18:17Z","score":60},{"id":"arxiv_1401.4794","title":"On the numerical radii of $2\\times2$ complex matrices","authors":[{"name":"L. Z. Gevorgyan"}],"abstract":"The numerical radius of the general $2\\times2$ complex matrix is calculated.","source":"arXiv","year":2014,"language":"en","subjects":["math.SP"],"url":"https://arxiv.org/abs/1401.4794","pdf_url":"https://arxiv.org/pdf/1401.4794","is_open_access":true,"published_at":"2014-01-20T05:52:28Z","score":58},{"id":"ss_34a81b66fc5852fcd4ba4db1cdf1565cf0aeb7be","title":"Sur la théorie spectrale des métriques intégrables sur une surface de Riemann compacte","authors":[{"name":"Mounir Hajli"}],"abstract":"We continue the study of the spectral theory associated to integrable metrics, started in our previous paper arXiv:1301.1793 [math.SP]. We introduce the notion of 1-integrable metric on line-bundles on a compact Riemann surface. We extend the spectral theory of generalized Laplacians to line-bundles equipped with 1-integrable metrics. As an application, we recover the following identity: [\\zeta'_{\\Delta_{\\bar{\\mathcal{O}(m)}_\\infty}}(0)=T_g\\bigl((\\p^1,\\omega_\\infty); \\bar{\\mathcal{O}(m)}_\\infty \\bigr),] obtained using direct computations in arXiv:1301.1792 [math.NT].","source":"Semantic Scholar","year":2013,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/34a81b66fc5852fcd4ba4db1cdf1565cf0aeb7be","is_open_access":true,"citations":2,"published_at":"","score":57.06},{"id":"arxiv_1308.4422","title":"On Pleijel's nodal domain theorem","authors":[{"name":"Jean Bourgain"}],"abstract":"A slight improvement of Pleijel's estimate on the number of nodal domains is obtained, exploiting a refinement of the Faber-Krahn inequality and packing density of discs.","source":"arXiv","year":2013,"language":"en","subjects":["math.SP"],"url":"https://arxiv.org/abs/1308.4422","pdf_url":"https://arxiv.org/pdf/1308.4422","is_open_access":true,"published_at":"2013-08-20T20:05:45Z","score":57},{"id":"arxiv_1203.4730","title":"Optimization of quasi-normal eigenvalues for Krein-Nudelman strings","authors":[{"name":"Illya M. Karabash"}],"abstract":"The paper is devoted to optimization of resonances for Krein strings with total mass and statical moment constraints. The problem is to design for a given $α\\in \\R$ a string that has a resonance on the line $α+ ı\\R$ with a minimal possible modulus of the imaginary part. We find optimal resonances and strings explicitly.","source":"arXiv","year":2012,"language":"en","subjects":["math.SP","math.OC"],"doi":"10.1007/s00020-012-2014-4","url":"https://arxiv.org/abs/1203.4730","pdf_url":"https://arxiv.org/pdf/1203.4730","is_open_access":true,"published_at":"2012-03-01T16:00:06Z","score":56},{"id":"arxiv_1201.3424","title":"The Spectral Theory of Tensors (Rough Version)","authors":[{"name":"Liqun Qi"}],"abstract":"This is a survey of the spectral theory of tensors.","source":"arXiv","year":2012,"language":"en","subjects":["math.SP"],"url":"https://arxiv.org/abs/1201.3424","pdf_url":"https://arxiv.org/pdf/1201.3424","is_open_access":true,"published_at":"2012-01-17T04:15:33Z","score":56},{"id":"arxiv_1008.3284","title":"Scattering theory for CMV matrices: uniqueness, Helson--Szegő and Strong SzegŐ theorems","authors":[{"name":"L. Golinskii"},{"name":"A. Kheifets"},{"name":"F. Peherstorfer"},{"name":"P. Yuditskii"}],"abstract":"We develop a scattering theory for CMV matrices, similar to the Faddeev--Marchenko theory. A necessary and sufficient condition is obtained for the uniqueness of the solution of the inverse scattering problem. We also obtain two sufficient conditions for the uniqueness, which are connected with the Helson--Szeg\\H o and the Strong Szeg\\H o theorems. The first condition is given in terms of the boundedness of a transformation operator associated to the CMV matrix. In the second case this operator has a determinant. In both cases we characterize Verblunsky parameters of the CMV matrices, corresponding spectral measures and scattering functions.","source":"arXiv","year":2010,"language":"en","subjects":["math.SP","math.CA"],"url":"https://arxiv.org/abs/1008.3284","pdf_url":"https://arxiv.org/pdf/1008.3284","is_open_access":true,"published_at":"2010-08-19T12:08:00Z","score":54},{"id":"arxiv_1012.3068","title":"Multiple tunnel effect for dispersive waves on a star-shaped network: an explicit formula for the spectral representation","authors":[{"name":"Felix Ali Mehmeti"},{"name":"Robert Haller-Dintelmann"},{"name":"Virginie Régnier"}],"abstract":"We consider the Klein-Gordon equation on a star-shaped network composed of n half-axes connected at their origins. We add a potential which is constant but different on each branch. The corresponding spatial operator is self-adjoint and we state explicit expressions for its resolvent and its resolution of the identity in terms of generalized eigenfunctions. This leads to a generalized Fourier type inversion formula in terms of an expansion in generalized eigenfunctions. Further we prove the surjectivity of the associated transformation, thus showing that it is in fact a spectral representation. The characteristics of the problem are marked by the non-manifold character of the star-shaped domain. Therefore the approach via the Sturm-Liouville theory for systems is not well-suited. The considerable effort to construct explicit formulas involving the tunnel effect generalized eigenfunctions is justified for example by the perspective to study the influence of tunnel effect on the L-infinity-time decay.","source":"arXiv","year":2010,"language":"en","subjects":["math.AP"],"url":"https://arxiv.org/abs/1012.3068","pdf_url":"https://arxiv.org/pdf/1012.3068","is_open_access":true,"published_at":"2010-12-14T16:07:03Z","score":54},{"id":"ss_14603b724320c02896be9b9134934fc789a43152","title":"On a class of non-self-adjoint periodic eigenproblems with boundary and interior singularities","authors":[{"name":"L. Boulton"},{"name":"M. Levitin"},{"name":"M. Marletta"}],"abstract":"We prove that the spectrum of a certain PT-symmetric periodic problem is purely real. Our results extend to a larger class of potentials those recently found by Brian Davies [math.SP/0702122] and John Weir [arXiv:0711.1371].","source":"Semantic Scholar","year":2007,"language":"en","subjects":["Mathematics"],"doi":"10.1016/J.JDE.2010.08.010","url":"https://www.semanticscholar.org/paper/14603b724320c02896be9b9134934fc789a43152","pdf_url":"https://doi.org/10.1016/j.jde.2010.08.010","is_open_access":true,"citations":15,"published_at":"","score":51.45},{"id":"ss_36523c34f419e40f210a909f9f0701385b7b9edc","title":"A PT-symmetric periodic problem with boundary and interior singularities","authors":[{"name":"L. Boulton"},{"name":"M. Levitin"},{"name":"M. Marletta"}],"abstract":"","source":"Semantic Scholar","year":2007,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/36523c34f419e40f210a909f9f0701385b7b9edc","is_open_access":true,"citations":9,"published_at":"","score":51.27},{"id":"arxiv_0801.0172","title":"On a class of non-self-adjoint periodic eigenproblems with boundary and interior singularities","authors":[{"name":"Lyonell Boulton"},{"name":"Michael Levitin"},{"name":"Marco Marletta"}],"abstract":"We prove that the spectrum of a certain PT-symmetric periodic problem is purely real. Our results extend to a larger class of potentials those recently found by Brian Davies [math.SP/0702122] and John Weir [arXiv:0711.1371].","source":"arXiv","year":2007,"language":"en","subjects":["math.SP","math.CA"],"url":"https://arxiv.org/abs/0801.0172","pdf_url":"https://arxiv.org/pdf/0801.0172","is_open_access":true,"published_at":"2007-12-30T23:54:52Z","score":51},{"id":"arxiv_math/0701674","title":"On Roots of Eigenpolynomials for Degenerate Exactly-Solvable Differential Operators","authors":[{"name":"Tanja Bergkvist"},{"name":"Jan-Erik Bjork"}],"abstract":"In this paper we partially settle our conjecture from [1] (math.SP/0701143) on roots of eigenpolynomials for degenerate exactly-solvable operators. Namely, for any such operator, we establish a lower bound (which supports our conjecture) for the largest modulus of the roots of its unique and monic eigenpolynomial as its degree tends to infinity. The main theorem below thus extends earlier results obtained in [1] for a more restrictive class of operators.","source":"arXiv","year":2007,"language":"en","subjects":["math.SP"],"url":"https://arxiv.org/abs/math/0701674","pdf_url":"https://arxiv.org/pdf/math/0701674","is_open_access":true,"published_at":"2007-01-24T10:00:23Z","score":51}],"total":1363817,"page":1,"page_size":20,"sources":["arXiv","Semantic Scholar","CrossRef"],"query":"math.SP"}