Kreĭn's trace formula and the spectral shift function
نویسندگان
چکیده
منابع مشابه
Krĕin’s Trace Formula and the Spectral Shift Function
Let A,B be two selfadjoint operators whose difference B −A is trace class. Krĕın proved the existence of a certain function ξ ∈ L1(R) such that tr[f (B)−f(A)] = ∫ Rf (x)ξ(x)dx for a large set of functions f . We give here a new proof of this result and discuss the class of admissible functions. Our proof is based on the integral representation of harmonic functions on the upper half plane and a...
متن کاملScattering matrix, phase shift, spectral shift and trace formula for one-dimensional dissipative Schrödinger-type operators
The paper is devoted to Schrödinger operators on bounded intervals of the real axis with dissipative boundary conditions. In the framework of the Lax-Phillips scattering theory the asymptotic behaviour of the phase shift is investigated in detail and its relation to the spectral shift is discussed. In particular, the trace formula and the Birman-Krein formula are verified directly. The results ...
متن کاملThe spectral side of Arthur's trace formula.
The trace formula is one of the most important tools in the theory of automorphic forms. It was invented in the 1950's by Selberg, who mostly studied the case of hyperbolic surfaces, and was later on developed extensively by Arthur in the generality of an adelic quotient of a reductive group over a number field. Here we provide an explicit expression for the spectral side, improving Arthur's fi...
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 کاملOn the Spectral Side of the Arthur Trace Formula
Let G be a connected reductive algebraic group defined over Q and let G(A) be the group of points of G with values in the ring of adèles of Q. Then G(Q) embeds diagonally as a discrete subgroup of G(A). Let G(A) be the intersection of the kernels of the maps x 7→ |χ(x)|, x ∈ G(A), where χ ranges over the group X(G)Q of characters of G defined over Q. Then the (noninvariant) trace formula of Art...
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: International Journal of Mathematics and Mathematical Sciences
سال: 2001
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171201004318