Self-adjoint integral operator for bounded nonlocal transport

Spectral Theorem for Bounded Self-adjoint Operators

Diagonalization is one of the most important topics one learns in an elementary linear algebra course. Unfortunately, it only works on finite dimensional vector spaces, where linear operators can be represented by finite matrices. Later, one encounters infinite dimensional vector spaces (spaces of sequences, for example), where linear operators can be thought of as ”infinite matrices”. Extendin...

The Laplace operator is essentially self-adjoint

Order Properties of Bounded Self-adjoint Operators1

Triple variational principles for self-adjoint operator functions

Article history: Received 13 June 2013 Accepted 3 September 2015 Available online 19 January 2016 Communicated by L. Gross MSC: primary 49R05 secondary 47A56, 47A10

Ozaki's conditions for general integral operator

Assume that $mathbb{D}$ is the open unit disk. Applying Ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{G}(alpha)$ and $mathcal{F}(mu)$ as follows begin{equation*}  mathcal{G}(alpha):=left{fin mathcal{A}:mathfrak{Re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right) <1+frac{alpha }{2},quad 0<alphaleq1right}, end{equation*} and begin{equation*}  ma...