Inequalities for eigenvalues of selfadjoint operators
نویسندگان
چکیده
منابع مشابه
Inequalities for the eigenvalues of non-selfadjoint Jacobi operators
We prove Lieb-Thirring-type bounds on eigenvalues of non-selfadjoint Jacobi operators, which are nearly as strong as those proven previously for the case of selfadjoint operators by Hundertmark and Simon. We use a method based on determinants of operators and on complex function theory, extending and sharpening earlier work of Borichev, Golinskii and Kupin.
متن کاملPayne-polya-weinberger Type Inequalities for Eigenvalues of Nonelliptic Operators
Let denote the Laplacian in the Euclidean space. The classic upper estimates, independent of the domain, for the gaps of eigenvalues of − , (− )2 and (− )k(k ≥ 3) were studied extensively by many mathematicians, cf. Payne, Polya and Weinberger [16], Hile and Yeh [10], Chen and Qian [2], Guo [8] etc.. The asymptotic behaviors of eigenvalues for degenerate elliptic operators were considered by Be...
متن کاملNumber of Eigenvalues for a Class of Non-selfadjoint Schrödinger Operators
In this article, we prove the finiteness of the number of eigenvalues for a class of Schrödinger operators H = −∆ + V (x) with a complex-valued potential V (x) on R, n ≥ 2. If IV is sufficiently small, IV ≤ 0 and IV 6= 0, we show that N(V ) = N(RV )+k, where k is the multiplicity of the zero resonance of the selfadjoint operator−∆+RV and N(W ) the number of eigenvalues of −∆+W , counted accordi...
متن کاملSome Slater Type Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces
Some inequalities of the Slater type for convex functions of selfad-joint operators in Hilbert spaces H under suitable assumptions for the involved operators are given. Amongst others, it is shown that if A is a positive definite operator with Sp (A) ⊂ [m, M ] and f is convex and has a continuous derivative on [m, M ] , then for any x ∈ H with x = 1 the following inequality holds: 0 ≤ f Af ′ (A...
متن کاملLieb-Thirring type inequalities for non-selfadjoint perturbations of magnetic Schrödinger operators
Let H := H0 + V and H⊥ := H0,⊥ + V be respectively perturbations of the free Schrödinger operators H0 on L2 ( R2d+1 ) and H0,⊥ on L2 ( R2d ) , d ≥ 1 with constant magnetic field of strength b > 0, and V is a complex relatively compact perturbation. We prove Lieb-Thirring type inequalities for the discrete spectrum ofH andH⊥. In particular, these estimates give a priori information on the distri...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1990
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1990-0943604-8