ZEROS OF THE WRONSKIAN AND RENORMALIZED OSCILLATION THEORY By F. GESZTESY, B. SIMON, and G. TESCHL
نویسندگان
چکیده
For general Sturm-Liouville operators with separated boundary conditions, we prove the following: If E1,2 2 R and if u1,2 solve the differential equation Huj = Ejuj, j = 1, 2 and respectively satisfy the boundary condition on the left/right, then the dimension of the spectral projection P(E1,E2)(H) of H equals the number of zeros of the Wronskian of u1 and u2.
منابع مشابه
Zeros of the Wronskian and Renormalized Oscillation Theory
For general Sturm-Liouville operators with separated boundary conditions, we prove the following: If E1,2 ∈ R and if u1,2 solve the differential equation Huj = Ejuj , j = 1, 2 and respectively satisfy the boundary condition on the left/right, then the dimension of the spectral projection P(E1,E2)(H) of H equals the number of zeros of the Wronskian of u1 and u2.
متن کاملRenormalized Oscillation Theory for Dirac Operators
Oscillation theory for one-dimensional Dirac operators with separated boundary conditions is investigated. Our main theorem reads: If λ0,1 ∈ R and if u, v solve the Dirac equation Hu = λ0u, Hv = λ1v (in the weak sense) and respectively satisfy the boundary condition on the left/right, then the dimension of the spectral projection P(λ0,λ1)(H) equals the number of zeros of the Wronskian of u and ...
متن کاملOscillation Theory and Renormalized Oscillation Theory for Jacobi Operators
We provide a comprehensive treatment of oscillation theory for Jacobi operators with separated boundary conditions. Our main results are as follows: If u solves the Jacobi equation (Hu)(n) = a(n)u(n + 1) + a(n − 1)u(n − 1) − b(n)u(n) = λu(n), λ ∈ R (in the weak sense) on an arbitrary interval and satisfies the boundary condition on the left or right, then the dimension of the spectral projectio...
متن کاملGains from diversification on convex combinations: A majorization and stochastic dominance approach
By incorporating both majorization theory and stochastic dominance theory, this paper presents a general theory and a unifying framework for determining the diversification preferences of risk-averse investors and conditions under which they would unanimously judge a particular asset to be superior. In particular, we develop a theory for comparing the preferences of different convex combination...
متن کاملImproved immunogenicity of tetanus toxoid by Brucella abortus S19 LPS adjuvant.
BACKGROUND Adjuvants are used to increase the immunogenicity of new generation vaccines, especially those based on recombinant proteins. Despite immunostimulatory properties, the use of bacterial lipopolysaccharide (LPS) as an adjuvant has been hampered due to its toxicity and pyrogenicity. Brucella abortus LPS is less toxic and has no pyrogenic properties compared to LPS from other gram negati...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1996