## Remling, Christian

Compute Distance To:
 Author ID: remling.christian Published as: Remling, Christian Homepage: https://math.ou.edu/~cremling/ External Links: MGP · Google Scholar · MathOverflow · dblp
 Documents Indexed: 47 Publications since 1996, including 2 Books Reviewing Activity: 16 Reviews Co-Authors: 20 Co-Authors with 20 Joint Publications 555 Co-Co-Authors
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### Co-Authors

 27 single-authored 3 Behncke, Horst 2 Hur, Injo 2 Kiselev, Alexander A. 2 Poltoratski, Alexei G. 2 Scarbrough, Kyle 1 Ben Amor, Ali 1 Christ, Michael 1 Damanik, David 1 de Snoo, Hendrik S. V. 1 Fischer, Andreas 1 Grudsky, Sergei Mikhailovich 1 Hassi, Seppo 1 Hinton, Don Barker 1 Killip, Rowan 1 Kriecherbauer, Thomas 1 Krutikov, Denis 1 Mcbride, Matt 1 Ong, Darren C. 1 Rybkin, Alexei 1 Simon, Barry
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### Serials

 8 Communications in Mathematical Physics 4 Proceedings of the American Mathematical Society 4 Transactions of the American Mathematical Society 2 Journal of Mathematical Analysis and Applications 2 Duke Mathematical Journal 2 Integral Equations and Operator Theory 2 Journal of Approximation Theory 2 Journal of Differential Equations 2 Journal of Functional Analysis 2 Journal of the London Mathematical Society. Second Series 2 Mathematical Physics, Analysis and Geometry 2 Journal of Spectral Theory 1 Applicable Analysis 1 Helvetica Physica Acta 1 Journal of Mathematical Physics 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Nachrichten 1 Mathematische Zeitschrift 1 IMRN. International Mathematics Research Notices 1 Mathematical Research Letters 1 Annals of Mathematics. Second Series 1 De Gruyter Studies in Mathematics
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### Fields

 37 Ordinary differential equations (34-XX) 27 Operator theory (47-XX) 16 Quantum theory (81-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 Partial differential equations (35-XX) 4 Difference and functional equations (39-XX) 2 Functions of a complex variable (30-XX) 2 Functional analysis (46-XX) 1 Measure and integration (28-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 General topology (54-XX)

### Citations contained in zbMATH Open

43 Publications have been cited 481 times in 282 Documents Cited by Year
The absolutely continuous spectrum of Jacobi matrices. Zbl 1235.47032
Remling, Christian
2011
Schrödinger operators and de Branges spaces. Zbl 1054.34019
Remling, Christian
2002
The absolute continuous spectrum of one-dimensional Schrödinger operators with decaying potentials. Zbl 0908.34067
Remling, Christian
1998
The absolutely continuous spectrum of one-dimensional Schrödinger operators. Zbl 1139.81036
Remling, Christian
2007
Reflectionless Herglotz functions and Jacobi matrices. Zbl 1183.47026
Poltoratski, Alexei; Remling, Christian
2009
The spectrum of differential operators of order $$2n$$ with almost constant coefficients. Zbl 0990.34070
Behncke, Horst; Hinton, Don; Remling, Christian
2001
Spectral analysis of higher order differential operators. I: General properties of the $$M$$-function. Zbl 0922.34068
Remling, Christian
1998
Spectral analysis of higher-order differential operators. II: Fourth-order equations. Zbl 0930.34061
Remling, Christian
1999
Schrödinger operators with sparse potentials: asymptotics of the Fourier transform of the spectral measure. Zbl 1161.81378
Krutikov, Denis; Remling, Christian
2001
Spectral theory of canonical systems. Zbl 1401.37004
Remling, Christian
2018
Effective perturbation methods for one-dimensional Schrödinger operators. Zbl 0921.34076
Kiselev, Alexander; Remling, Christian; Simon, Barry
1999
The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials. Zbl 0892.34075
Christ, Michael; Kiselev, Alexander; Remling, Christian
1997
Direct and inverse spectral theory of one-dimensional Schrödinger operators with measures. Zbl 1107.34064
Amor, Ali Ben; Remling, Christian
2005
Bounds on embedded singular spectrum for one-dimensional Schrödinger operators. Zbl 0931.34067
Remling, Christian
2000
Uniform asymptotic integration of a family of linear differential systems. Zbl 0995.34045
Behncke, Horst; Remling, Christian
2001
Inverse spectral theory for one-dimensional Schrödinger operators: The $$A$$ function. Zbl 1087.34004
Remling, Christian
2003
Asymptotic integration of linear differential equations. Zbl 0883.47041
Behncke, Horst; Remling, Christian
1997
Schrödinger operators with many bound states. Zbl 1114.34065
Damanik, David; Remling, Christian
2007
Essential spectrum and $$L_ 2$$-solutions of one-dimensional Schrödinger operators. Zbl 0858.34073
Remling, Christian
1996
Approximation results for reflectionless Jacobi matrices. Zbl 1225.47033
Poltoratski, Alexei; Remling, Christian
2011
A probabilistic approach to one-dimensional Schrödinger operators with sparse potentials. Zbl 0878.34071
Remling, Christian
1997
Generalized reflection coefficients. Zbl 1312.47039
Remling, Christian
2015
The absolutely continuous spectrum of discrete canonical systems. Zbl 1163.39007
Fischer, Andreas; Remling, Christian
2009
Relationships between the $$m$$-function and subordinate solutions of second order differential operators. Zbl 0878.34070
Remling, Christian
1997
Some Schrödinger operators with power-decaying potentials and pure point spectrum. Zbl 0896.34071
Remling, Christian
1997
Embedded singular continuous spectra for one-dimensional Schrödinger operators. Zbl 0918.34074
Remling, Christian
1999
Topological properties of reflectionless Jacobi matrices. Zbl 1272.47042
Remling, Christian
2013
Subordinate solutions and spectral measures of canonical systems. Zbl 0967.34073
Hassi, Seppo; Remling, Christian; de Snoo, Henk
2000
Uniqueness of reflectionless Jacobi matrices and the Denisov-Rakhmanov theorem. Zbl 1218.42011
Remling, Christian
2011
Finite gap potentials and WKB asymptotics for one-dimensional Schrödinger operators. Zbl 1017.81015
Kriecherbauer, Thomas; Remling, Christian
2001
Schrödinger operators with decaying potentials: some counterexamples. Zbl 1009.81019
Remling, Christian
2000
Geometric characterization of singular self-adjoint boundary conditions for Hamiltonian systems. Zbl 0872.34010
Remling, Christian
1996
Discrete and embedded eigenvalues for one-dimensional Schrödinger operators. Zbl 1131.39019
Remling, Christian
2007
The inverse scattering transform for the KdV equation with step-like singular Miura initial profiles. Zbl 1328.35199
Grudsky, Sergei; Remling, Christian; Rybkin, Alexei
2015
Toda maps, cocycles, and canonical systems. Zbl 1434.37037
Remling, Christian
2019
Generalized Toda flows. Zbl 1419.37057
Ong, Darren C.; Remling, Christian
2019
Universal bounds on spectral measures of one-dimensional Schrödinger operators. Zbl 1044.34044
Remling, Christian
2003
The essential spectrum of canonical systems. Zbl 1457.34122
Remling, Christian; Scarbrough, Kyle
2020
Oscillation theory and semibounded canonical systems. Zbl 1477.34110
Remling, Christian; Scarbrough, Kyle
2020
One-dimensional Schrödinger operators with decaying potentials. Zbl 0989.34069
Remling, Christian
1999
Finite propagation speed and kernel estimates for Schrödinger operators. Zbl 1121.81050
Remling, Christian
2007
Spectral theory of ordinary differential operators using the $$m$$-function. (Spektraltheorie gewöhnlicher Differentialoperatoren mit Hilfe der $$m$$-Funktion.) Zbl 0851.34023
Remling, Christian
1996
The Marchenko representation of reflectionless Jacobi and Schrödinger operators. Zbl 1355.34125
Hur, Injo; McBride, Matt; Remling, Christian
2016
The essential spectrum of canonical systems. Zbl 1457.34122
Remling, Christian; Scarbrough, Kyle
2020
Oscillation theory and semibounded canonical systems. Zbl 1477.34110
Remling, Christian; Scarbrough, Kyle
2020
Toda maps, cocycles, and canonical systems. Zbl 1434.37037
Remling, Christian
2019
Generalized Toda flows. Zbl 1419.37057
Ong, Darren C.; Remling, Christian
2019
Spectral theory of canonical systems. Zbl 1401.37004
Remling, Christian
2018
The Marchenko representation of reflectionless Jacobi and Schrödinger operators. Zbl 1355.34125
Hur, Injo; McBride, Matt; Remling, Christian
2016
Generalized reflection coefficients. Zbl 1312.47039
Remling, Christian
2015
The inverse scattering transform for the KdV equation with step-like singular Miura initial profiles. Zbl 1328.35199
Grudsky, Sergei; Remling, Christian; Rybkin, Alexei
2015
Topological properties of reflectionless Jacobi matrices. Zbl 1272.47042
Remling, Christian
2013
The absolutely continuous spectrum of Jacobi matrices. Zbl 1235.47032
Remling, Christian
2011
Approximation results for reflectionless Jacobi matrices. Zbl 1225.47033
Poltoratski, Alexei; Remling, Christian
2011
Uniqueness of reflectionless Jacobi matrices and the Denisov-Rakhmanov theorem. Zbl 1218.42011
Remling, Christian
2011
Reflectionless Herglotz functions and Jacobi matrices. Zbl 1183.47026
Poltoratski, Alexei; Remling, Christian
2009
The absolutely continuous spectrum of discrete canonical systems. Zbl 1163.39007
Fischer, Andreas; Remling, Christian
2009
The absolutely continuous spectrum of one-dimensional Schrödinger operators. Zbl 1139.81036
Remling, Christian
2007
Schrödinger operators with many bound states. Zbl 1114.34065
Damanik, David; Remling, Christian
2007
Discrete and embedded eigenvalues for one-dimensional Schrödinger operators. Zbl 1131.39019
Remling, Christian
2007
Finite propagation speed and kernel estimates for Schrödinger operators. Zbl 1121.81050
Remling, Christian
2007
Direct and inverse spectral theory of one-dimensional Schrödinger operators with measures. Zbl 1107.34064
Amor, Ali Ben; Remling, Christian
2005
Inverse spectral theory for one-dimensional Schrödinger operators: The $$A$$ function. Zbl 1087.34004
Remling, Christian
2003
Universal bounds on spectral measures of one-dimensional Schrödinger operators. Zbl 1044.34044
Remling, Christian
2003
Schrödinger operators and de Branges spaces. Zbl 1054.34019
Remling, Christian
2002
The spectrum of differential operators of order $$2n$$ with almost constant coefficients. Zbl 0990.34070
Behncke, Horst; Hinton, Don; Remling, Christian
2001
Schrödinger operators with sparse potentials: asymptotics of the Fourier transform of the spectral measure. Zbl 1161.81378
Krutikov, Denis; Remling, Christian
2001
Uniform asymptotic integration of a family of linear differential systems. Zbl 0995.34045
Behncke, Horst; Remling, Christian
2001
Finite gap potentials and WKB asymptotics for one-dimensional Schrödinger operators. Zbl 1017.81015
Kriecherbauer, Thomas; Remling, Christian
2001
Bounds on embedded singular spectrum for one-dimensional Schrödinger operators. Zbl 0931.34067
Remling, Christian
2000
Subordinate solutions and spectral measures of canonical systems. Zbl 0967.34073
Hassi, Seppo; Remling, Christian; de Snoo, Henk
2000
Schrödinger operators with decaying potentials: some counterexamples. Zbl 1009.81019
Remling, Christian
2000
Spectral analysis of higher-order differential operators. II: Fourth-order equations. Zbl 0930.34061
Remling, Christian
1999
Effective perturbation methods for one-dimensional Schrödinger operators. Zbl 0921.34076
Kiselev, Alexander; Remling, Christian; Simon, Barry
1999
Embedded singular continuous spectra for one-dimensional Schrödinger operators. Zbl 0918.34074
Remling, Christian
1999
One-dimensional Schrödinger operators with decaying potentials. Zbl 0989.34069
Remling, Christian
1999
The absolute continuous spectrum of one-dimensional Schrödinger operators with decaying potentials. Zbl 0908.34067
Remling, Christian
1998
Spectral analysis of higher order differential operators. I: General properties of the $$M$$-function. Zbl 0922.34068
Remling, Christian
1998
The absolutely continuous spectrum of one-dimensional Schrödinger operators with decaying potentials. Zbl 0892.34075
Christ, Michael; Kiselev, Alexander; Remling, Christian
1997
Asymptotic integration of linear differential equations. Zbl 0883.47041
Behncke, Horst; Remling, Christian
1997
A probabilistic approach to one-dimensional Schrödinger operators with sparse potentials. Zbl 0878.34071
Remling, Christian
1997
Relationships between the $$m$$-function and subordinate solutions of second order differential operators. Zbl 0878.34070
Remling, Christian
1997
Some Schrödinger operators with power-decaying potentials and pure point spectrum. Zbl 0896.34071
Remling, Christian
1997
Essential spectrum and $$L_ 2$$-solutions of one-dimensional Schrödinger operators. Zbl 0858.34073
Remling, Christian
1996
Geometric characterization of singular self-adjoint boundary conditions for Hamiltonian systems. Zbl 0872.34010
Remling, Christian
1996
Spectral theory of ordinary differential operators using the $$m$$-function. (Spektraltheorie gewöhnlicher Differentialoperatoren mit Hilfe der $$m$$-Funktion.) Zbl 0851.34023
Remling, Christian
1996
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### Cited by 217 Authors

 24 Damanik, David 20 Remling, Christian 18 Behncke, Horst 17 Simon, Barry 12 Zinchenko, Maxim 10 Ong, Darren C. 10 Yuditskii, Peter Meerovich 9 Breuer, Jonathan 9 Silva, Luis O. 9 Woracek, Harald 8 Christiansen, Jacob Stordal 8 Gesztesy, Fritz 8 Nyamwala, Fredrick Oluoch 8 Safronov, Oleg 8 Sun, Huaqing 8 Toloza, Julio H. 7 Hinton, Don Barker 7 Kiselev, Alexander A. 7 Lukic, Milivoje 7 Shi, Yuming 6 Last, Yoram 6 Liu, Wencai 6 Naboko, Serguei N. 5 Acharya, Keshav Raj 5 Baranov, Anton D. 5 Eckhardt, Jonathan 5 Goldstein, Michael 5 Hur, Injo 5 Killip, Rowan 5 Seifert, Christian 4 Eichinger, Benjamin 4 Kostenko, Aleksey S. 4 Sakhnovich, Alexander L. 4 Tcheremchantsev, Serguei 4 Teschl, Gerald 3 Bodine, Sigrun I. 3 Chen, Shaozhu 3 Christ, Michael 3 del Río Castillo, Rafael René 3 Fillman, Jake 3 Guo, Shuzheng 3 Jitomirskaya, Svetlana Yakovlevna 3 Lubinsky, Doron S. 3 Marchetti, Domingos H. U. 3 Poltoratski, Alexei G. 3 Rybkin, Alexei 3 VandenBoom, Tom 3 Wreszinski, Walter F. 2 Ambogo, David Otieno 2 Avila, Artur 2 Belov, Yurii S. 2 Bessonov, Roman V. 2 de Snoo, Hendrik S. V. 2 Denisov, Sergey A. 2 Exner, Pavel 2 Fischer, Andreas 2 Golénia, Sylvain 2 Hassi, Seppo 2 Jakšić, Vojkan 2 Johnson, Russell Allan 2 Kaluzhny, Uri 2 Krüger, Helge 2 Kurbatov, Vitaliĭ Gennad’evich 2 Kurbatova, Irina Vital’evna 2 Laptev, Ari 2 Lenz, Daniel H. 2 Lindner, Marko 2 Lutz, Donald A. 2 Mandich, Marc-Adrien 2 Mcbride, Matt 2 Mogilevskii, Vadim 2 Nazarov, Fedor L. 2 Pearson, David B. 2 Pillet, Claude-Alain 2 Romanov, Roman V. 2 Ryckman, Eric 2 Shi, Guoliang 2 Simonov, Sergey A. 2 Stollmann, Peter 2 Sun, Jiong 2 Sun, Shurong 2 Suzuki, Masatoshi 2 Tchebotareva, Olga 2 Uribe, Alfredo 2 Winkler, Henrik 2 Zampogni, Luca 2 Zettl, Anton 1 Abakumov, Evgeny V. 1 Agure, John Ogonji 1 Alpan, Gökalp 1 Arov, Damir Zyamovich 1 Avdonin, Sergeĭ Anatol’evich 1 Baratchart, Laurent 1 Beckus, Siegfried 1 Bell, Jonathan 1 Bellavita, Carlo 1 Binder, Ilia A. 1 Blair, Matthew D. 1 Bohner, Martin J. 1 Bourget, Olivier ...and 117 more Authors
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### Cited in 78 Serials

 19 Communications in Mathematical Physics 18 Journal of Mathematical Analysis and Applications 18 Journal of Functional Analysis 12 Journal d’Analyse Mathématique 10 Integral Equations and Operator Theory 10 Journal of Differential Equations 10 Proceedings of the American Mathematical Society 10 Annales Henri Poincaré 8 Mathematische Nachrichten 7 Transactions of the American Mathematical Society 6 Journal of Mathematical Physics 6 Journal of Approximation Theory 6 Constructive Approximation 6 Linear Algebra and its Applications 6 Journal of Difference Equations and Applications 6 Mathematical Physics, Analysis and Geometry 6 Complex Analysis and Operator Theory 6 Journal of Spectral Theory 4 Letters in Mathematical Physics 4 Advances in Mathematics 4 Duke Mathematical Journal 4 Inventiones Mathematicae 4 Journal of Computational and Applied Mathematics 4 Journal of the American Mathematical Society 4 St. Petersburg Mathematical Journal 3 Rocky Mountain Journal of Mathematics 3 Abstract and Applied Analysis 3 Annals of Mathematics. Second Series 2 Israel Journal of Mathematics 2 Journal of Statistical Physics 2 Mathematical Notes 2 Nonlinearity 2 Arkiv för Matematik 2 Reviews in Mathematical Physics 2 Monatshefte für Mathematik 2 Geometric and Functional Analysis. GAFA 2 Journal of Mathematical Sciences (New York) 2 Documenta Mathematica 2 Computational Methods and Function Theory 2 Oberwolfach Reports 2 Operators and Matrices 2 Science China. Mathematics 2 ISRN Mathematical Analysis 2 Analysis and Mathematical Physics 2 Bulletin of Mathematical Sciences 1 Applicable Analysis 1 Journal of Mathematical Biology 1 Mathematical Methods in the Applied Sciences 1 Acta Mathematica 1 Annales de l’Institut Fourier 1 Archiv der Mathematik 1 Bulletin de la Société Mathématique de France 1 Collectanea Mathematica 1 Kyungpook Mathematical Journal 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Memoirs of the American Mathematical Society 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Ergodic Theory and Dynamical Systems 1 Acta Mathematica Hungarica 1 Acta Applicandae Mathematicae 1 Physica D 1 The Journal of Geometric Analysis 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Expositiones Mathematicae 1 Journal of Dynamics and Differential Equations 1 Applied and Computational Harmonic Analysis 1 Sbornik: Mathematics 1 Journal of the European Mathematical Society (JEMS) 1 Qualitative Theory of Dynamical Systems 1 Computational Methods in Applied Mathematics 1 Complex Variables and Elliptic Equations 1 Discrete and Continuous Dynamical Systems. Series S 1 Annals of Functional Analysis 1 Journal of Function Spaces 1 Transactions of the American Mathematical Society. Series B
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### Cited in 30 Fields

 155 Operator theory (47-XX) 128 Ordinary differential equations (34-XX) 67 Quantum theory (81-XX) 55 Partial differential equations (35-XX) 33 Dynamical systems and ergodic theory (37-XX) 33 Difference and functional equations (39-XX) 28 Harmonic analysis on Euclidean spaces (42-XX) 26 Functional analysis (46-XX) 25 Functions of a complex variable (30-XX) 14 Statistical mechanics, structure of matter (82-XX) 7 Combinatorics (05-XX) 7 Special functions (33-XX) 6 Approximations and expansions (41-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 4 Potential theory (31-XX) 3 Algebraic geometry (14-XX) 3 Measure and integration (28-XX) 3 Probability theory and stochastic processes (60-XX) 3 Numerical analysis (65-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Convex and discrete geometry (52-XX) 2 Information and communication theory, circuits (94-XX) 1 Real functions (26-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 Mechanics of particles and systems (70-XX) 1 Biology and other natural sciences (92-XX)