Asymptotic normality of eigenvalues of random ordinary differential operators
نویسندگان
چکیده
منابع مشابه
On the Approximation of Isolated Eigenvalues of Ordinary Differential Operators
We extend a result of Stolz and Weidmann on the approximation of isolated eigenvalues of singular Sturm–Liouville and Dirac operators by the eigenvalues of regular operators.
متن کاملComputing eigenvalues of ordinary differential equations
Discretisations of differential eigenvalue problems have a sensitivity to perturbations which is asymptotically least as h→ 0 when the differential equation is in first order system form. Both second and fourth order accurate discretisations of the first order system are straightforward to derive and lead to generalised eigenvalue problems of the form (A(h)− λB(h))v = 0 , where both A and B are...
متن کاملSpectrality of Ordinary Differential Operators
We prove the long standing conjecture in the theory of two-point boundary value problems that completeness and Dunford’s spectrality imply Birkhoff regularity. In addition we establish the even order part of S.G.Krein’s conjecture that dissipative differential operators are Birkhoff-regular and give sharp estimate of the norms of spectral projectors in the odd case. Considerations are based on ...
متن کاملAsymptotic Formulae for the Eigenvalues of a Two-parameter Ordinary Differential Equation of the Second Order(')
We consider a two-point boundary value problem associated with an ordinary differential equation defined over the unit interval and containing the two parameters A and p. If for each real p. we denote the zzith eigenvalue of our system by Am(/j.), then it is known that Am(/j.) is real analytic in — co ...
متن کاملOn the Eigenvalues of Certain Canonical Higher-Order Ordinary Differential Operators
We consider the operator of taking the 2pth derivative of a function with zero boundary conditions for the function and its first p − 1 derivatives at two distinct points. Our main result provides an asymptotic formula for the eigenvalues and resolves a question on the appearance of certain regular numbers in the eigenvalue sequences for p = 1 and p = 3.
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: Applications of Mathematics
سال: 1991
ISSN: 0862-7940,1572-9109
DOI: 10.21136/am.1991.104465