Eigenvalues of Schrödinger operators on finite and infinite intervals
نویسندگان
چکیده
We consider a Sturm–Liouville operator with an integrable potential q on the unit interval I = [ 0 , 1 ] . Schrödinger real compactly supported half line and line, where this coincides vanishes outside I. determine relationships between eigenvalues of such operators obtain estimates in terms potentials.
منابع مشابه
On the number of eigenvalues of Schrödinger operators with complex potentials
We study the eigenvalues of Schrödinger operators with complex potentials in odd space dimensions. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity.
متن کاملOn the Finite Rank of Bounded Semi-infinite Hankel Operators
Bounded, semi-infinite Hankel matrices of finite rank over the space l of square-summable sequences occur frequently in classical analysis and engineering applications. The notion of finite rank often appears under different contexts and the literature is diverse. The first part of this paper reviews some elegant, classic criteria and establish connections among the various characterizations of...
متن کاملsome properties of fuzzy hilbert spaces and norm of operators
in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...
15 صفحه اولOn Extended Eigenvalues of Operators
A complex number λ is an extended eigenvalue of an operator A if there is a nonzero operator X such that AX = λXA. We characterize the the set of extended eigenvalues for operators acting on finite dimensional spaces, finite rank operators, Jordan blocks, and C0 contractions. We also describe the relationship between the extended eigenvalues of an operator A and its powers. We derive some appli...
متن کاملOn the finite rank and finite-dimensional representation of bounded semi-infinite Hankel operators
Bounded, semi-infinite Hankel matrices of finite rank over the space 2 of square-summable sequences occur frequently in classical analysis and engineering applications. The notion of finite rank often appears under different contexts and the literature is diverse. The first part of this paper reviews some elegant, classical criteria and establishes connections among the various characterization...
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: Mathematische Nachrichten
سال: 2021
ISSN: ['1522-2616', '0025-584X']
DOI: https://doi.org/10.1002/mana.201900511