@article{ASENS_1981_4_14_1_27_0, author = {Colin de Verdi\`ere, Yves}, title = {Une formule de traces pour l{\textquoteright}op\'erateur de {Schr\"odinger} dans $\mathbb {R}^3$}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {27--39}, publisher = {Elsevier}, volume = {4e s{\'e}rie, 14}, number = {1}, year = {1981}, doi = {10.24033/asens.1395}, mrnumber = {82g:35088}, zbl = {0482.35068}, language = {fr}, url = {https://www.numdam.org/articles/10.24033/asens.1395/} }
TY - JOUR AU - Colin de Verdière, Yves TI - Une formule de traces pour l’opérateur de Schrödinger dans $\mathbb {R}^3$ JO - Annales scientifiques de l'École Normale Supérieure PY - 1981 SP - 27 EP - 39 VL - 14 IS - 1 PB - Elsevier UR - https://www.numdam.org/articles/10.24033/asens.1395/ DO - 10.24033/asens.1395 LA - fr ID - ASENS_1981_4_14_1_27_0 ER -
%0 Journal Article %A Colin de Verdière, Yves %T Une formule de traces pour l’opérateur de Schrödinger dans $\mathbb {R}^3$ %J Annales scientifiques de l'École Normale Supérieure %D 1981 %P 27-39 %V 14 %N 1 %I Elsevier %U https://www.numdam.org/articles/10.24033/asens.1395/ %R 10.24033/asens.1395 %G fr %F ASENS_1981_4_14_1_27_0
Colin de Verdière, Yves. Une formule de traces pour l’opérateur de Schrödinger dans $\mathbb {R}^3$. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 14 (1981) no. 1, pp. 27-39. doi : 10.24033/asens.1395. https://www.numdam.org/articles/10.24033/asens.1395/
[A-S] Spectral and Scattering Theory for Schrödinger Operators (Arch. Rat. Mech. Anal., vol. 40, 1971, p. 281-311). | MR | Zbl
et ,[B] Scattered Plane waves, Spectral Asymptotics and Trace Formulas in Exterior Problems (Dokl. Akad. Nauk S.S.S.R., vol. 197, 1971, p. 591-595). | MR | Zbl
,[B-G-M] Le spectre d'une variété riemannienne (Lecture Notes in Math., vol. 194, 1971). | MR | Zbl
, et ,[B-K] On the Theory of wave Operators and Scattering Operators (Dokl. Akad. Nauk S.S.S.R., vol. 144, 1962, p. 475-478). | MR | Zbl
et ,[CV] Spectre du laplacien et longueurs des géodésiques périodiques II (Compositio Mathematica, vol. 27, 1973, p. 159-184). | Numdam | MR | Zbl
,[F-Z] KdV Equation : a Completely Integrable Hamiltonian System (Funct. Anal. and Appl. vol. 5, 1971, p. 280-288). | Zbl
et ,[G-M-G-T] A Family of Optimal Conditions for the Absence of Bound States in a Potential. Studies in Math. Phys., LIEB, SIMON et WIGHTMANN, éd., Princeton, 1976, p. 169-194. | Zbl
, , et ,[J-K] Asymptotic behaviour of the Scattering Phase for Exterior Domains (Comm. P.D.E., vol. 3, 1978, p. 1165-1195). | MR | Zbl
et ,[K-M] The Spectrum of Hill's Equation (Invent. Math., vol. 30, 1975, p. 217-254). | MR | Zbl
et ,[L-P1] Scattering Theory for Automorphic Functions (Annals Math. Studies, 1976, Princeton). | MR | Zbl
et ,[L-P 2] The Time Delay Operator and a Related Trace Formula. Topics in Functional Analysis, GOHBERG et M. KAC, ed., Academic Press, 1978, p. 197-215. | MR | Zbl
et ,[L-T] Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian... Studies in Math. Phys., LIEB, SIMON et WIGHTMANN, éd., Princeton, 1976, p. 269-304. | Zbl
et ,[MR] An Analogue of Weyl's Theorem for Unbounded Domains I, II et III (Duke Math. J., vol. 45, p. 183-196 et 513-536 ; vol. 46, 1979, p. 725-731). | Zbl
et ,[N] Non Central Potentiels : the Generalized Levinson Theorem and the Structure of the Spectrum (J. Math. Phys., vol. 18, 1977, p. 1348-1357). | MR
,[R-S] Scattering Theory, Academic Press, 1979. | Zbl
et ,[S 1] Quantum Mechanics for Hamiltonians defined as Quadratic Forms, Princeton, 1971. | Zbl
,[S 2] Trace Ideals and their Applications, Cambridge, 1979. | MR | Zbl
,[S 3] On the Number of Bound States of the Two-Body Schrödinger Operators. A review. Studies in Math. Phys., LIEB, SIMON et WIGHTMANN, éd., Princeton, 1976, p. 305-326. | Zbl
,[Z-K] The Born Expansion in non Relativistic Quantum Theory, I (Nuovo Cimento, vol. 10, 1958, p. 1078-1087). | MR | Zbl
et ,- Existence of resonances for Schrödinger operators on hyperbolic space, Analysis PDE, Volume 17 (2024) no. 6, p. 2077 | DOI:10.2140/apde.2024.17.2077
- On the trace of the wave group and regularity of potentials, Annales de l'Institut Fourier, Volume 73 (2023) no. 4, p. 1453 | DOI:10.5802/aif.3538
- Spectral asymptotics for the Schrödinger operator with a non-decaying potential, Asymptotic Analysis, Volume 130 (2022) no. 3-4, p. 335 | DOI:10.3233/asy-211754
- Compactness of iso-resonant potentials for Schrödinger operators in dimensions one and three, Transactions of the American Mathematical Society, Volume 374 (2021) no. 6, p. 4481 | DOI:10.1090/tran/8361
- Trace Formulas for Schrödinger Operators with Complex Potentials, Russian Journal of Mathematical Physics, Volume 27 (2020) no. 1, p. 82 | DOI:10.1134/s1061920820010082
- Resonant Rigidity for Schrödinger Operators in Even Dimensions, Annales Henri Poincaré, Volume 20 (2019) no. 5, p. 1543 | DOI:10.1007/s00023-019-00791-6
- Trace asymptotics for fractional Schrödinger operators, Journal of Functional Analysis, Volume 266 (2014) no. 2, p. 514 | DOI:10.1016/j.jfa.2013.10.021
- Short-time Asymptotics for Semigroups of Diffusion Type and Beyond, Geometric Methods in Physics (2013), p. 415 | DOI:10.1007/978-3-0348-0448-6_38
- Heat kernel asymptotics for magnetic Schrödinger operators, Journal of Mathematical Physics, Volume 54 (2013) no. 11 | DOI:10.1063/1.4829061
- Inverse Problems, Trace Formulae for Discrete Schrödinger Operators, Annales Henri Poincaré, Volume 13 (2012) no. 4, p. 751 | DOI:10.1007/s00023-011-0141-0
- Schwartz Kernel asymptotics and regularized traces of diffusion semigroups, Functional Analysis and Its Applications, Volume 44 (2010) no. 1, p. 76 | DOI:10.1007/s10688-010-0010-5
- Parametrix, heat kernel asymptotics, and regularized trace of the diffusion semigroup, Proceedings of the Steklov Institute of Mathematics, Volume 271 (2010) no. 1, p. 228 | DOI:10.1134/s0081543810040176
- Асимптотика интегрального ядра и регуляризованный след диффузионной полугруппы, Функциональный анализ и его приложения, Volume 44 (2010) no. 1, p. 90 | DOI:10.4213/faa2975
- Two-sided estimates for the trace of the difference of two semigroups, Functional Analysis and Its Applications, Volume 43 (2009) no. 3, p. 184 | DOI:10.1007/s10688-009-0026-x
- Двусторонние оценки для следа разности пары полугрупп, Функциональный анализ и его приложения, Volume 43 (2009) no. 3, p. 26 | DOI:10.4213/faa2958
- Parametrix, kernel asymptotics, and regularized trace for the diffusion semigroup, Doklady Mathematics, Volume 77 (2008) no. 3, p. 424 | DOI:10.1134/s1064562408030289
- The Schrödinger operator: Perturbation determinants, the spectral shift function, trace identities, and all that, Functional Analysis and Its Applications, Volume 41 (2007) no. 3, p. 217 | DOI:10.1007/s10688-007-0019-6
- Оператор Шрeдингера: определители возмущения, функция спектрального сдвига, тождества следов и прочее, Функциональный анализ и его приложения, Volume 41 (2007) no. 3, p. 60 | DOI:10.4213/faa2868
- Compactness of isospectral potentials, Transactions of the American Mathematical Society, Volume 357 (2004) no. 5, p. 1717 | DOI:10.1090/s0002-9947-04-03813-9
- Trace Formulae and High Energy Asymptotics for the Stark Operator, Communications in Partial Differential Equations, Volume 28 (2003) no. 3-4, p. 817 | DOI:10.1081/pde-120020498
- SMOOTHNESS AND HIGH ENERGY ASYMPTOTICS OF THE SPECTRAL SHIFT FUNCTION IN MANY-BODY SCATTERING, Communications in Partial Differential Equations, Volume 27 (2002) no. 11-12, p. 2139 | DOI:10.1081/pde-120016156
- Fonction spectrale pour des perturbations relativement Hilbert–Schmidt, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, Volume 332 (2001) no. 10, p. 887 | DOI:10.1016/s0764-4442(01)01916-4
- Generalized scattering phase for long range perturbations of elliptic operators, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, Volume 333 (2001) no. 9, p. 845 | DOI:10.1016/s0764-4442(01)02144-9
- Cluster Properties of One Particle Schrödinger Operators. II, Reviews in Mathematical Physics, Volume 10 (1998) no. 05, p. 627 | DOI:10.1142/s0129055x98000203
- References, Quantum Chaos and Mesoscopic Systems (1997), p. 297 | DOI:10.1007/978-94-015-8792-1_15
- Trace distributions associated to the Schrödinger operator, Journal d'Analyse Mathématique, Volume 59 (1992) no. 1, p. 133 | DOI:10.1007/bf02790222
- High energy asymptotics for the total scattering phase in potential scattering theory, Functional-Analytic Methods for Partial Differential Equations, Volume 1450 (1990), p. 187 | DOI:10.1007/bfb0084906
- Breit-Wigner formulas for the scattering phase and the total scattering cross-section in the semi-classical limit, Communications in Mathematical Physics, Volume 121 (1989) no. 2, p. 323 | DOI:10.1007/bf01217809
- Semi-classical asymptotics for local spectral densities and time delay problems in scattering processes, Journal of Functional Analysis, Volume 80 (1988) no. 1, p. 124 | DOI:10.1016/0022-1236(88)90069-9
- The Relation Between Quantum Mechanics And Classical Mechanics: A Survey Of Some Mathematical Aspects, Chaotic Behavior in Quantum Systems, Volume 120 (1985), p. 37 | DOI:10.1007/978-1-4613-2443-0_3
- Semi-classical bounds for resolvents of schrödinger operators and asymptotics for scattering phases, Communications in Partial Differential Equations, Volume 9 (1984) no. 10, p. 1017 | DOI:10.1080/03605308408820355
- Spectral Theory for Riemannian Manifolds with Cusps and a Related Trace Formula, Mathematische Nachrichten, Volume 111 (1983) no. 1, p. 197 | DOI:10.1002/mana.19831110109
- Propagation of Singularities and the Scattering Matrix, Singularities in Boundary Value Problems (1981), p. 169 | DOI:10.1007/978-94-009-8434-9_8
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