Suppose is a nonnegative, locally integrable, radial function on , which is nonincreasing in . Set when and . Given and , we show there exists so that for all , if and only if exists with for all dyadic cubes Q, where . This result is used to refine recent estimates of C.L. Fefferman and D.H. Phong on the distribution of eigenvalues of Schrödinger operators.
Soit une fonction radiale, non négative, localement intégrable sur , qui ne s’accroît pas en . Posons où et . Étant donné et , nous démontrons qu’il existe de sorte que pour tout , si et seulement si, existe avec pour tout cube dyadique , où .
On se sert de ce résultat pour raffiner des approximations récentes de la part de C.L. Fefferman et D.H. Phong de la distribution de valeurs propres d’opérateurs de Schrödinger.
@article{AIF_1986__36_4_207_0, author = {Kerman, R. and Sawyer, Eric T.}, title = {The trace inequality and eigenvalue estimates for {Schr\"odinger} operators}, journal = {Annales de l'Institut Fourier}, pages = {207--228}, publisher = {Imprimerie Durand}, address = {28 - Luisant}, volume = {36}, number = {4}, year = {1986}, doi = {10.5802/aif.1074}, mrnumber = {88b:35150}, zbl = {0591.47037}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1074/} }
TY - JOUR TI - The trace inequality and eigenvalue estimates for Schrödinger operators JO - Annales de l'Institut Fourier PY - 1986 DA - 1986/// SP - 207 EP - 228 VL - 36 IS - 4 PB - Imprimerie Durand PP - 28 - Luisant UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1074/ UR - https://www.ams.org/mathscinet-getitem?mr=88b:35150 UR - https://zbmath.org/?q=an%3A0591.47037 UR - https://doi.org/10.5802/aif.1074 DO - 10.5802/aif.1074 LA - en ID - AIF_1986__36_4_207_0 ER -
Kerman, R.; Sawyer, Eric T. The trace inequality and eigenvalue estimates for Schrödinger operators. Annales de l'Institut Fourier, Volume 36 (1986) no. 4, pp. 207-228. doi : 10.5802/aif.1074. https://aif.centre-mersenne.org/articles/10.5802/aif.1074/
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