Applications

Random matrices in 2D, Laplacian growth and operator theory

“…In short, putting together the above comments we can state the following result: the canonical representations: For a complete proof see for instance Chapter VIII of [127] and the references cited there. The above dictionary is remarkable in many ways.…”

“…They will be serve as Hilbert space counterparts for the study of moving boundaries in two dimensions. The reader is advised to consult the monographs [127,131] is then well-defined, independent of the ordering in the functional calculus, and possesses the algebraic identities of the Jacobian…”

Approximation Results for Reflectionless Jacobi Matrices

“…See [3,5,12,15] for earlier applications of this basic method, and also [4] for related uses of the ξ function. Our presentation here follows [12,Sections 5,6] very closely, with some additional material added. We only sketch most of the proofs here and refer the reader to this reference for full details.…”

Seminormal systems of operators in Clifford environments

“…We should also mention that the theory of seminormal operators was initially developed for pairs (X, Y ) of self-adjoint operators in L(H) rather than a single operator T ∈ L(H). Assuming that X = Re(T ) and Y = Im(T ), i.e., X is the real part of T and Y is the imaginary part of T , from For a comprehensive historical perspective on the development of the theory of seminormal operators and the relationship with the theory of subnormal operators we refer to the monographs by Putnam [36], Clancey [8], Xia [43], Martin and Putinar [28], and Conway [9]. Our goal is to single out and motivate what we believe to be the most natural counterparts of the previous equations and requirements in a multidimensional setting, i.e., for systems of operators.…”