Quantitative inductive estimates for Green’s functions of non-self-adjoint matrices

Resolvent estimates for non-self-adjoint operators via semi-groups

We consider a non-self-adjoint h-pseudodifferential operator P in the semi-classical limit (h → 0). If p is the leading symbol, then under suitable assumptions about the behaviour of p at infinity, we know that the resolvent (z − P )−1 is uniformly bounded for z in any compact set not intersecting the closure of the range of p. Under a subellipticity condition, we show that the resolvent extend...

Spectral Properties of Random Non-self-adjoint Matrices and Operators

We describe some numerical experiments which determine the degree of spectral instability of medium size randomly generated matrices which are far from self-adjoint. The conclusion is that the eigenvalues are likely to be intrinsically uncomputable for similar matrices of a larger size. We also describe a stochastic family of bounded operators in infinite dimensions for almost all of which the ...

Ela Norm Estimates for Functions of Two Non-commuting Matrices

A class of matrix valued analytic functions of two non-commuting matrices is considered. A sharp norm estimate is established. Applications to matrix and differential equations are also discussed.

Norm estimates for functions of two non-commuting matrices

Application of the Norm Estimates for Univalence of Analytic Functions

By using norm estimates of the pre-Schwarzian derivatives for certain family of analytic functions, we shall give simple sufficient conditions for univalence of analytic functions.