Proof of the Payne-Pólya-Weinberger conjecture
نویسندگان
چکیده
منابع مشابه
Payne-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 کاملPayne - Weinberger eigenvalue estimate for wedge domains on spheres ∗
A Faber-Krahn type argument gives a sharp lower estimate for the first Dirichlet eigenvalue for subdomains of wedge domains in spheres, generalizing the inequality for the plane, found by Payne and Weinberger. An application is an alternative proof to the finiteness of a Brownian motion capture time estimate. Many lower estimates for the first Dirichlet eigenvalue of a domain stem from an inequ...
متن کاملPartial proof of Graham Higman's conjecture related to coset diagrams
Graham Higman has defined coset diagrams for PSL(2,ℤ). These diagrams are composed of fragments, and the fragments are further composed of two or more circuits. Q. Mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. Higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...
متن کاملPayne-polya-weinberger, Hile-protter and Yang’s Inequalities for Dirichlet Laplace Eigenvalues on Integer Lattices
In this paper, we prove some analogues of Payne-Polya-Weinberger, HileProtter and Yang’s inequalities for Dirichlet (discrete) Laplace eigenvalues on any subset in the integer lattice Z. This partially answers a question posed by Chung and Oden [CO00].
متن کاملA short proof of the maximum conjecture in CR dimension one
In this paper and by means of the extant results in the Tanaka theory, we present a very short proof in the specific case of CR dimension one for Beloshapka's maximum conjecture. Accordingly, we prove that each totally nondegenerate model of CR dimension one and length >= 3 has rigidity. As a result, we observe that the group of CR automorphisms associated with each of such models contains onl...
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: Bulletin of the American Mathematical Society
سال: 1991
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1991-16016-7