Some sturm theory
نویسندگان
چکیده
منابع مشابه
An Indefinite Sturm Theory
We will use the variational approach to (0.1) as described in [2] and we will stick to the notations of that paper. Given the complex n-dimensional Hermitian space (C, 〈·, ·〉), for any m ∈ N let H m := H(J,C) be the Sobolev space of all H-maps from J := [0, 1] into C. A derivative dependent Hermitian form is the form Ω(x)[u] = Pm i,j=0〈D u(x), ωi,j(x)D u(x)〉, where, each ωi,j is a smooth path o...
متن کاملA Counterexample in Sturm-Liouville Completeness Theory
We give an example of an indefinite weight Sturm-Liouville problem whose eigenfunctions form a Riesz basis under Dirichlet boundary conditions but not under anti-periodic boundary conditions.
متن کاملOn Generalization of Sturm-Liouville Theory for Fractional Bessel Operator
In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...
متن کاملOn The Eigenvalues of Some Vectorial Sturm-Liouville Eigenvalue Problems
The author tries to derive the asymptotic expression of the large eigevalues of some vectorial Sturm-Liouville differential equations. A precise description for the formula of the square root of the large eiegnvalues up to the O(1/n)-term is obtained.
متن کاملSome Analytical and Numerical Consequences of Sturm Theorems
The Sturm comparison theorems for second order ODEs are classical results from which information on the properties of the zeros of special functions can be obtained. Sturm separation and comparison theorems are also available for difference-differential systems under oscillatory conditions. The separation theorem provides interlacing information for zeros of some special functions and the compa...
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: Journal d'Analyse Mathématique
سال: 1981
ISSN: 0021-7670,1565-8538
DOI: 10.1007/bf02803340