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Math.","publisher":"Amer. Math. Soc., Providence, RI", "year": "2007", "url": "https://doi.org/10.1090/conm/445/08611", "author": [ "Timo Weidl" ], "authors": [ {"first" : "Timo", "last" : "Weidl"} ], "volume": "445","pages": "337--357","abstract": "We discuss modifications and generalisations of the celebrated bound on the singular values of operators of the type a(x)b(i∇) by M. Cwikel.", "mrclass" : "47G10 (35J10 46B70 47N50 81Q10)", "mrreviewer" : "Serge C. Richard", "mrnumber" : "2381904", "doi" : "10.1090/conm/445/08611", "bibtexKey": "MR2381904" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/28e309fc1ea55fba4facb5ec5ad000989/elkepeter", "tags" : [ "IADM","Weidl","Spectral","estimates" ], "intraHash" : "8e309fc1ea55fba4facb5ec5ad000989", "interHash" : "9ff7cfcf0d541aa55cbdc0ce24d3d4c2", "label" : "Spectral estimates for two-dimensional Schrödinger operators with application to quantum layers", "user" : "elkepeter", "description" : "", "date" : "2022-03-30 16:33:37", "changeDate" : "2023-04-21 12:36:24", "count" : 2, "pub-type": "article", "journal": "Comm. Math. Phys.", "year": "2007", "url": "https://doi.org/10.1007/s00220-007-0318-z", "author": [ "Hynek Kovar\\'ık","Semjon Vugalter","Timo Weidl" ], "authors": [ {"first" : "Hynek", "last" : "Kovar\\'ık"}, {"first" : "Semjon", "last" : "Vugalter"}, {"first" : "Timo", "last" : "Weidl"} ], "volume": "275","number": "3","pages": "827--838","abstract": "A logarithmic type Lieb-Thirring inequality fort wo-dimensional Schrödinger operators is established. The result is applied to prove spectral estimates on trapped modes in quantum layers.", "mrclass" : "81Q10 (35J10 35P15 47F05)", "mrreviewer" : "Pavel V. Exner", "mrnumber" : "2336366", "issn" : "0010-3616", "doi" : "10.1007/s00220-007-0318-z", "bibtexKey": "MR2336366" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/281a22819f19677675334cfa64c8ed4e7/elkepeter", "tags" : [ "geisinger","iadm","spectral","estimates","weidl" ], "intraHash" : "81a22819f19677675334cfa64c8ed4e7", "interHash" : "30aa9eb360b3dc8e2f38dd542b86ea97", "label" : "Sharp spectral estimates in domains of infinite volume.", "user" : "elkepeter", "description" : "", "date" : "2021-11-04 06:38:22", "changeDate" : "2023-04-21 13:37:46", "count" : 3, "pub-type": "article", "journal": "Reviews in Mathematical Physics.", "year": "2011", "url": "", "author": [ "Leander Geisinger","Timo Weidl" ], "authors": [ {"first" : "Leander", "last" : "Geisinger"}, {"first" : "Timo", "last" : "Weidl"} ], "volume": "23","number": "6","pages": "615-641","abstract": "We consider the Dirichlet Laplace operator on open, quasi-bounded domains of infinite volume. For such domains semiclassical spectral estimates based on the phase-space volume - and therefore on the volume of the domain - must fail. Here we present a method how one can nevertheless prove uniform bounds on eigenvalues and eigenvalue means which are sharp in the semiclassical limit. We give examples in horn-shaped regions and so-called spiny urchins. Some results are extended to Schrödinger operators defined on quasi-bounded domains with Dirichlet boundary conditions.", "language" : "English", "doi" : "10.1142/S0129055X11004394", "bibtexKey": "geisinger2011sharp" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2907a0e555dff55149a3093c1235b9c78/elkepeter", "tags" : [ "equations","iadm","dispersive","wirth","estimates","wave" ], "intraHash" : "907a0e555dff55149a3093c1235b9c78", "interHash" : "b5e8823b3b94ba0877b631ab128a7bd9", "label" : "Energy inequalities and dispersive estimates for wave equations with time-dependent coefficients", "user" : "elkepeter", "description" : "", "date" : "2021-10-21 07:21:58", "changeDate" : "2021-10-21 05:21:58", "count" : 3, "pub-type": "article", "journal": "Rend. Istit. Mat. Univ. Trieste", "year": "2010", "url": "", "author": [ "Jens Wirth" ], "authors": [ {"first" : "Jens", "last" : "Wirth"} ], "volume": "42","number": "suppl.","pages": "205--219", "mrclass" : "35L15 (35B40 35B45)", "mrreviewer" : "Atanas G. Stefanov", "fjournal" : "Rendiconti dell'Istituto di Matematica dell'Università di\r\n Trieste. An International Journal of Mathematics", "mrnumber" : "2760485", "issn" : "0049-4704", "bibtexKey": "MR2760485" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2c18b3ecdac7ee7d09a2a6564f8574c40/elkepeter", "tags" : [ "Decay","Wirth","Estimates","Girardi" ], "intraHash" : "c18b3ecdac7ee7d09a2a6564f8574c40", "interHash" : "6b3bf33fc37152191c52db19be42aaef", "label" : "Decay Estimates for a Klein-Gordon Model with Time-Periodic Coeffizients", "user" : "elkepeter", "description" : "", "date" : "2021-10-13 15:08:57", "changeDate" : "2021-10-21 04:59:38", "count" : 3, "pub-type": "incollection", "booktitle": "Anomalies in Partial Differential Equations","series": "INdAM Series","publisher":"Springer", "year": "2021", "url": "", "author": [ "Giovanni Girardi","Jens Wirth" ], "authors": [ {"first" : "Giovanni", "last" : "Girardi"}, {"first" : "Jens", "last" : "Wirth"} ], "editor": [ "Massimo Cicognani","Daniele del Santo","Alberto Parmeggiani","Michael Reissig" ], "editors": [ {"first" : "Massimo", "last" : "Cicognani"}, {"first" : "Daniele", "last" : "del Santo"}, {"first" : "Alberto", "last" : "Parmeggiani"}, {"first" : "Michael", "last" : "Reissig"} ], "volume": "43", "isbn" : "978-3-030-61346-4", "doi" : "10.1007/978-3-030-61346-4_14", "bibtexKey": "girardi2021decay" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2480eb8d27436d1813f64a75501305a78/elkepeter", "tags" : [ "iadm","Ruszkowski","Heisenberg","Spectral","Kovarik","estimates","weidl","Laplacian" ], "intraHash" : "480eb8d27436d1813f64a75501305a78", "interHash" : "a744d4ee0c0570857beee23ca1ced4b3", "label" : "Spectral estimates for the Heisenberg Laplacian on cylinders.", "user" : "elkepeter", "description" : "", "date" : "2021-10-08 20:07:59", "changeDate" : "2021-10-13 11:54:00", "count" : 2, "pub-type": "article", "journal": "Functional Analysis and Operator Theory for Quantum Physics, EMS Series of Congress Reports, J. Dittrich, et al. (eds.)", "year": "2017", "url": "", "author": [ "Hynek Kovarik","Bartosch Ruszkowski","Timo Weidl" ], "authors": [ {"first" : "Hynek", "last" : "Kovarik"}, {"first" : "Bartosch", "last" : "Ruszkowski"}, {"first" : "Timo", "last" : "Weidl"} ], "pages": "433-446","abstract": "\"In this paper the authors consider the Heisenberg Laplacian in a domain Ω⊂ℝ3 with Dirichlet boundary conditions, formally given by\r\nA(Ω)=−X21−X22,\r\nwhere\r\nX1=∂x1+x22∂x3,X2=∂x2−x12∂x3.\r\n The main result of the paper is a uniform upper bound with remainder of the quantity\r\nTr(A(Ω)−λ)−,\r\nthat is, the sum of all eigenvalues of A(Ω) smaller than λ, counted according to their multiplicities. \r\n Previous and optimal results on the leading term were known from [A. M. Hansson and A. Laptev, in Groups and analysis, 100\u2013115, London Math. Soc. Lecture Note Ser., 354, Cambridge Univ. Press, Cambridge, 2008; MR2528463], and improved estimates were obtained in [H. Kovařík and T. Weidl, Proc. Roy. Soc. Edinburgh Sect. A 145 (2015), no. 1, 145\u2013160; MR3304579], where it was proved that for any bounded domain Ω⊂ℝ3 there exists a constant C(Ω)>0 such that\r\nTr(A(Ω)−λ)−≤max0,|Ω|96λ3−C(Ω)λ2.\r\n\r\n In this paper, the authors improve the above estimate for cylindrical domains of the form Ω=ω×(a,b), where ω⊂ℝ2 is an open, simply connected, bounded set. Their main result (Theorem 2.3) is an estimate of the form\r\nTr(A(Ω)−λ)−≤max0,|Ω|96λ3−D(Ω)λ(2c+5)/(c+2),(1)\r\nwhere c is the best Hardy constant for ω, and the constant D(Ω) depends explicitly on the cylindrical domain Ω. Notice that the correction term in (1) is of order larger than λ2. \r\n For cylinders Ω=ω×(a,b) with convex cross-section ω, the above estimate reads:\r\nTr(A(Ω)−λ)−≤max0,|Ω|96λ3−λ2+1/427⋅35/2|Ω|R(ω)3/2,\r\nwhere R(ω) is the Euclidean in-radius of ω. \r\n The main techniques employed are the relation of A(Ω) with the magnetic Laplacian (with constant magnetic field) and Hardy inequalities.\"", "bibtexKey": "kovarik2017spectral" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2e886c8eeab9e7c3ad9d8e8d6159d5729/elkepeter", "tags" : [ "IADM","Weidl","estimates" ], "intraHash" : "e886c8eeab9e7c3ad9d8e8d6159d5729", "interHash" : "89ba981f84e320c8f59f6a207eda8104", "label" : "Estimates for operators of the form b(x)a(D)\r\n in non-powerlike ideals.", "user" : "elkepeter", "description" : "", "date" : "2021-09-08 20:35:09", "changeDate" : "2021-10-13 11:54:00", "count" : 2, "pub-type": "article", "journal": "St.-Petersburg Mathematical Journal", "year": "1994", "url": "", "author": [ "Timo Weidl" ], "authors": [ {"first" : "Timo", "last" : "Weidl"} ], "volume": "5","number": "5","pages": "907-923","abstract": "Some applications of nonpower interpolation functors to function spaces and to ideals of compact operators are discussed. Previously known conditions ensuring the boundedness and compactness of operators of the form b(x)a(D) are refined, and a \u201Cnonpower\u201D estimate for the asymptotic behavior of the singular numbers is given.", "language" : "English", "bibtexKey": "weidl1994estimates" } ] }