Accurate Spectral Asymptotics for periodic operators
Victor Ivrii (1999)
Journées équations aux dérivées partielles
Similarity:
Asymptotics with sharp remainder estimates are recovered for number of eigenvalues of operator crossing level as runs from to , . Here is periodic matrix operator, matrix is positive, periodic with respect to first copy of and decaying as second copy of goes to infinity, either belongs to a spectral gap of or is one its ends. These problems are first treated in papers of M. Sh. Birman, M. Sh. Birman-A. Laptev and M. Sh. Birman-T. Suslina.