CONCAVITY PROPERTIES OF KREIN’S SPECTRAL SHIFT FUNCTION
نویسندگان
چکیده
منابع مشابه
Monotonicity and Concavity Properties of the Spectral Shift Function
Let H0 and V (s) be self-adjoint, V, V ′ continuously differentiable in trace norm with V (s) ≥ 0 for s ∈ (s1, s2), and denote by {EH(s)(λ)}λ∈R the family of spectral projections of H(s) = H0+V (s). Then we prove for given μ ∈ R, that s 7−→ tr ( V ′(s)EH(s)((−∞, μ)) ) is a nonincreasing function with respect to s, extending a result of Birman and Solomyak. Moreover, denoting by ζ(μ, s) = ∫ μ −∞...
متن کاملConcavity of Eigenvalue Sums and the Spectral Shift Function
It is well known that the sum of negative (positive) eigenvalues of some finite Hermitian matrix V is concave (convex) with respect to V . Using the theory of the spectral shift function we generalize this property to self-adjoint operators on a separable Hilbert space with an arbitrary spectrum. More precisely, we prove that the spectral shift function integrated with respect to the spectral p...
متن کاملKrein Spectral Shift Function
A b s t r a c t . Let ~A,B be the Krein spectral shift function for a pair of operators A, B, with C = A B trace class. We establish the bound f F(I~A,B()~)I ) d,~ <_ f F ( 1 5 1 c l , o ( ) , ) l ) d A = ~ [F(j) F ( j 1 ) ] # j ( C ) , j= l where F is any non-negative convex function on [0, oo) with F(O) = 0 and #j (C) are the singular values of C. The choice F(t) = t p, p > 1, improves a rece...
متن کاملMeromorphic Continuation of the Spectral Shift Function
We obtain a representation of the derivative of the spectral shift function ξ(λ, h) in the framework of semi-classical ”black box” perturbations. Our representation implies a meromorphic continuation of ξ(λ, h) involving the semi-classical resonances. Moreover, we obtain a Weyl type asymptotics of the spectral shift function as well as a Breit-Wigner approximation in an interval (λ− δ, λ+ δ), 0...
متن کاملSome concavity properties for general integral operators
Let $C_0(alpha)$ denote the class of concave univalent functions defined in the open unit disk $mathbb{D}$. Each function $f in C_{0}(alpha)$ maps the unit disk $mathbb{D}$ onto the complement of an unbounded convex set. In this paper, we study the mapping properties of this class under integral operators.
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: Reviews in Mathematical Physics
سال: 1995
ISSN: 0129-055X,1793-6659
DOI: 10.1142/s0129055x95000098