Minimum eigenvalues for positive, Rockland operators
نویسندگان
چکیده
منابع مشابه
On the Eigenvalues of Positive Operators by Gian-carlo Rota
The classical theory of Frobenius-Perron concerning the distribution of eigenvalues of a matrix with non-negative elements has been variously extended to positive operators, that is, linear operators on function spaces transforming non-negative functions into non-negative functions. Since the classical work of Jentzsch (see bibliography), there have been two kinds of extensions : (a) it has bee...
متن کاملOn Positive Eigenvalues of One - Body Schrodinger Operators
The last twenty years have produced a rather extensive literature on the exact mathematical treatment of general features of the Schrodinger equation for one or many particles. One of the more intriguing questions concerns the presence of discrete eigenvalues of positive energy (that is square-integrable eigenfunctions with positive eigenvalues) . There is a highly non-rigorous but physically a...
متن کاملTransmission Eigenvalues for Elliptic Operators
A reduction of the transmission eigenvalue problem for multiplicative sign-definite perturbations of elliptic operators with constant coefficients to an eigenvalue problem for a non-selfadjoint compact operator is given. Sufficient conditions for the existence of transmission eigenvalues and completeness of generalized eigenstates for the transmission eigenvalue problem are derived. In the trac...
متن کاملEnclosure Theorems for Eigenvalues of Elliptic Operators
are to be considered when the coefficients a,-,-, b, and c are continuous real-valued functions with &=^0, c>0 in En. The ellipticity of L implies that the symmetric matrix (a,,) is everywhere positive definite. A "solution" u of Lu = 0 is supposed to be of class C1 and all derivatives involved in (1.1) are supposed to exist, be continuous, and satisfy Lu = 0 at every point. The eigenvalue prob...
متن کاملVariational Characterization for Eigenvalues of Dirac Operators
In this paper we give two diierent variational characterizations for the eigenvalues of H + V where H denotes the free Dirac operator and V is a scalar potential. The rst one is a min-max involving a Rayleigh quotient. The second one consists in minimizing an appropriate nonlinear functional. Both methods can be applied to potentials which have singularities as strong as the Coulomb potential.
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: Proceedings of the American Mathematical Society
سال: 1985
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1985-0792290-2