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In this follow-up on the work of Fefferman-Seco [FS] an improved condition for the discrete eigenvalues of the operator -d2 / dx2 + V(x) is established for V(x) satisfying certain hypotheses. The eigenvalue condition in [FS] establishes eigenvalues of this operator to within a small error. Through an obervation due to C. Fefferman, the order of accuracy can be improved if a certain condition is true. This paper improves on the result obtained in [FS] by showing that this condition does indeed hold.
Ho, Alan. "A note on eigenvalues of ordinary differential operators.." Revista Matemática Iberoamericana 13.2 (1997): 403-410. <http://eudml.org/doc/39537>.
@article{Ho1997, abstract = {In this follow-up on the work of Fefferman-Seco [FS] an improved condition for the discrete eigenvalues of the operator -d2 / dx2 + V(x) is established for V(x) satisfying certain hypotheses. The eigenvalue condition in [FS] establishes eigenvalues of this operator to within a small error. Through an obervation due to C. Fefferman, the order of accuracy can be improved if a certain condition is true. This paper improves on the result obtained in [FS] by showing that this condition does indeed hold.}, author = {Ho, Alan}, journal = {Revista Matemática Iberoamericana}, keywords = {Operadores diferenciales; Autovalores; ordinary differential operators; asymptotic formula; standard WKB method; eigenvalues}, language = {eng}, number = {2}, pages = {403-410}, title = {A note on eigenvalues of ordinary differential operators.}, url = {http://eudml.org/doc/39537}, volume = {13}, year = {1997}, }
TY - JOUR AU - Ho, Alan TI - A note on eigenvalues of ordinary differential operators. JO - Revista Matemática Iberoamericana PY - 1997 VL - 13 IS - 2 SP - 403 EP - 410 AB - In this follow-up on the work of Fefferman-Seco [FS] an improved condition for the discrete eigenvalues of the operator -d2 / dx2 + V(x) is established for V(x) satisfying certain hypotheses. The eigenvalue condition in [FS] establishes eigenvalues of this operator to within a small error. Through an obervation due to C. Fefferman, the order of accuracy can be improved if a certain condition is true. This paper improves on the result obtained in [FS] by showing that this condition does indeed hold. LA - eng KW - Operadores diferenciales; Autovalores; ordinary differential operators; asymptotic formula; standard WKB method; eigenvalues UR - http://eudml.org/doc/39537 ER -