Spectral flow as winding number and integral formulas
نویسندگان
چکیده
منابع مشابه
Spectral Flow as Winding Number and Integral Formulas
A general integral formula for the spectral flow of a path of unbounded selfadjoint Fredholm operators subject to certain summability conditions is derived from the interpretation of the spectral flow as a winding number.
متن کاملSpectral flow and winding number in von Neumann algebras
We define a new topology, weaker than the gap topology, on the space of selfadjoint operators affiliated to a semifinite von Neumann algebra and define the real-valued spectral flow for a continuous path of selfadjoint Breuer-Fredholm operators in terms of a generalization of the winding number. We compare our definition with Phillips’ analytical definition. Furthermore we prove the homotopy in...
متن کاملCauchy non-integral formulas
We study certain generalized Cauchy integral formulas for gradients of solutions to second order divergence form elliptic systems, which appeared in recent work by P. Auscher and A. Rosén. These are constructed through functional calculus and are in general beyond the scope of singular integrals. More precisely, we establish such Cauchy formulas for solutions u with gradient in weighted L2(R 1+...
متن کاملThe Prime Number Formulas
There are many proposed partial prime number formulas, however, no formula can generate all prime numbers. Here we show three formulas which can obtain the entire prime numbers set from the positive integers, based on the Möbius function plus the “omega” function, or the Omega function, or the divisor function. The history of searching for a prime number formula goes back to the ancient Egyptia...
متن کاملInstitute for Mathematical Physics Intermediate Inversion Formulas in Integral Geometry Intermediate Inversion Formulas in Integral Geometry
We solve the following \intermediate" problem of integral geometry: to reconstruct integrals of a function over p-dimensional planes in R n starting from its integrals over k-planes, where p < k. Some generalizations are also presented.
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: Proceedings of the American Mathematical Society
سال: 2007
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-07-08919-8