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Notices of the American Mathematical Society, ISSN 0002-9920, 08/2016, Volume 63, Issue 7, pp. 740 - 752
Journal Article
Journal d'Analyse Mathématique, ISSN 0021-7670, 1/2011, Volume 113, Issue 1, pp. 53 - 172
This paper has two main goals. First, we are concerned with a description of all self-adjoint extensions of the Laplacian $$ - \Delta {|_{C_0^\infty (\Omega... 
Abstract Harmonic Analysis | Mathematics | Functional Analysis | Dynamical Systems and Ergodic Theory | Analysis | Partial Differential Equations
Journal Article
2003, Cambridge studies in advanced mathematics, ISBN 0521753082, Volume 79, 114, v.
As a partner to Volume 1: Dimensional Continuous Models, this monograph provides a self-contained introduction to algebro-geometric solutions of completely... 
Differential equations, Nonlinear | Numerical solutions | Solitons
Book
Mathematische Annalen, ISSN 0025-5831, 8/2018, Volume 371, Issue 3, pp. 1255 - 1300
The spectral shift function of a pair of self-adjoint operators is expressed via an abstract operator-valued Titchmarsh–Weyl m-function. This general result is... 
Primary 35J10 | 47A55 | 47B10 | Mathematics | 35J15 | 47A10 | 47A40 | 47B25 | Secondary 35P20 | 35P25 | Mathematics, general | 81Q10 | 47F05 | MATHEMATICS | SCATTERING MATRICES | GENERALIZED RESOLVENTS | HIGHER-ORDER | BOUNDARY-VALUE-PROBLEMS | TRACE FORMULA | DOMAINS | PERTURBATION DETERMINANTS | ELLIPTIC-OPERATORS | SELF-ADJOINT EXTENSIONS | SCHRODINGER-OPERATORS
Journal Article
2003, CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS; 79. SER: SOLITON EQUATIONS AND THEIR...; V. 1., ISBN 9780521753074
Book
Advances in Mathematics, ISSN 0001-8708, 04/2017, Volume 311, pp. 569 - 597
We extend a result on renormalized oscillation theory, originally derived for Sturm–Liouville and Dirac-type operators on arbitrary intervals in the context of... 
Matrix oscillation theory | Hamiltonian systems | Sturm–Liouville and Dirac-type operators | Eigenvalue counting in essential spectral gaps | Sturm-Liouville and Dirac-type operators | ROTATION NUMBER | MATHEMATICS | DIRAC OPERATORS | 2 SINGULAR POINTS | M(LAMBDA) THEORY | ZEROS
Journal Article
2016, Contemporary Mathematicians, ISBN 9783319187983, 778
This is the second part of a two volume anthology comprising a selection of 49 articles that illustrate the depth, breadth and scope of Nigel Kalton's... 
Mathematics | Mathematicians | History of Mathematical Sciences | Applications of Mathematics | Functional Analysis
eBook
2016, Contemporary Mathematicians, ISBN 9783319187952, 769
This book is the first part of a two volume anthology comprising a selection of 49 articles that illustrate the depth, breadth and scope of Nigel Kalton's... 
Mathematics | Mathematicians | History of Mathematical Sciences | Applications of Mathematics | Functional Analysis
eBook
07/2016, Contemporary mathematicians, ISBN 9783319187952, Volume 1
This book is the first part of a two volume anthology comprising a selection of 49 articles that illustrate the depth, breadth and scope of Nigel Kalton's... 
Mathematicians
eBook
Opuscula Mathematica, ISSN 1232-9274, 2013, Volume 33, Issue 3, pp. 467 - 563
Opuscula Math. 33, 467-563 (2013) We systematically develop Weyl-Titchmarsh theory for singular differential operators on arbitrary intervals $(a,b) \subseteq... 
Positivity preserving and improving semigroups | Friedrichs and Krein extensions | Sturm-Liouville operators | Weyl-Titchmarsh theory | Distributional coefficients | distributional coefficients | positivity preserving and improving semigroups
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 07/2012, Volume 253, Issue 2, pp. 400 - 437
Under the assumption that V∈L2([0,π];dx), we derive necessary and sufficient conditions in terms of spectral data for (non-self-adjoint) Schrödinger operators... 
Periodic and antiperiodic boundary conditions | Riesz basis | Non-self-adjoint Hill operators | Secondary | Primary | BASIS PROPERTY | STURM-LIOUVILLE OPERATOR | ROOT FUNCTIONS | SPECTRAL DECOMPOSITIONS | SCALAR TYPE | ORDINARY DIFFERENTIAL-OPERATORS | POTENTIALS | HILL OPERATORS | MATHEMATICS | ALGEBRO-GEOMETRIC SOLUTIONS | EQUATION
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2009, Volume 247, Issue 10, pp. 2871 - 2896
The aim of this paper is twofold: First, we characterize an essentially optimal class of boundary operators Θ which give rise to self-adjoint Laplacians − Δ Θ... 
Nonlocal Robin Laplacians | Spectral analysis | Eigenvalue inequalities | Lipschitz domains | BOUNDARY-CONDITIONS | MONOTONICITY | LIPSCHITZ-DOMAINS | NEUMANN EIGENVALUES | MATHEMATICS | FABER-KRAHN INEQUALITY | PRINCIPAL EIGENVALUE | DIRICHLET | OPERATORS
Journal Article
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-503X, 03/2008, Volume 366, Issue 1867, pp. 1025 - 1054
Journal Article
Integral Equations and Operator Theory, ISSN 0378-620X, 6/2016, Volume 85, Issue 2, pp. 301 - 302
To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s00020-016-2290-5 
Analysis | Mathematics
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 10/2020, Volume 279, Issue 6, p. 108609
The principal objective in this paper is a new inverse approach to general Dirac-type systems of the formy′(x,z)=i(zJ+JV(x))y(x,z)(x≥0), where y=(y1,…,ym)⊤ and... 
Dirac-type systems | Matrix-valued potentials | Inverse problems
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 04/2015, Volume 143, Issue 4, pp. 1635 - 1649
The principal aim of this short note is to extend a recent result on Gaussian heat kernel bounds for self-adjoint L-2(Omega; d(n)x)-realizations, n is an... 
Heat kernel bounds | Green’s function bounds | Positivity preserving semigroups | Elliptic partial differential operators | Robin boundary conditions | MATHEMATICS | SEMIGROUPS | MATHEMATICS, APPLIED | Green's function bounds | elliptic partial differential operators | heat kernel bounds
Journal Article
Journal d'Analyse Mathématique, ISSN 0021-7670, 4/2014, Volume 122, Issue 1, pp. 229 - 287
Journal Article
Advances in Mathematics, ISSN 0001-8708, 10/2016, Volume 301, pp. 1022 - 1061
We investigate closed, symmetric L2(Rn)-realizations H of Schrödinger-type operators (−Δ+V)↾C0∞(Rn∖Σ) whose potential coefficient V has a countable number of... 
Self-adjointness | Deficiency indices | Strongly singular potentials | DIRAC-OPERATORS | ESSENTIAL SELFADJOINTNESS | BOUNDEDNESS | EXTENSION | SPECTRAL PROPERTIES | UNIQUENESS | SCATTERING THEORY | MATHEMATICS | ELLIPTIC DIFFERENTIAL OPERATORS | ABSORPTION | ESSENTIAL SELF-ADJOINTNESS
Journal Article