Javad Mashreghi

A primer on the Dirichlet Spaces

The Dirichlet space is one of the three fundamental Hilbert spaces of holomorphic functions on the unit disk. It boasts a rich and beautiful theory, yet at the same time remains a source of challenging open problems and a subject of active mathematical research. This book is the first systematic account of the Dirichlet space, assembling results previously only found in scattered research articles, and improving upon many of the proofs. Topics treated include: the Douglas and Carleson formulas for the Dirichlet integral, reproducing kernels, boundary behaviour and capacity, zero sets and uniqueness sets, multipliers, interpolation, Carleson measures, composition operators, local Dirichlet spaces, shift-invariant subspaces, and cyclicity. Special features include a self-contained treatment of capacity, including the strong-type inequality. The book will be valuable to researchers in function theory, and with over 100 exercises it is also suitable for self-study by graduate students.

Maps preserving the local spectrum of triple product of operators

Let denote the algebra of all bounded linear operators on a Banach space . Let and be infinite-dimensional complex Banach spaces, and fix two nonzero vectors and . Then we show that a surjective map satisfiesif and only if there exists a bijective mapping such that andwhere is a third root of unity.

MAPS PRESERVING THE LOCAL SPECTRUM OF PRODUCT OF OPERATORS

Let X and Y be infinite-dimensional complex Banach spaces, and

Weighted norm inequalities for de Branges-Rovnyak spaces and their applications

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Integral Means of the Logarithmic Derivative of Blaschke Products

( X ) (resp.

Strong Convergence of an Inexact Proximal Point Algorithm for Equilibrium Problems in Banach Spaces

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On mapping theorems for numerical range

( Y )) be the algebra of all bounded linear operators on X (resp. on Y ). For an operator T ∈

On the population model of the non-autonomous logistic equation of second order with period-two parameters

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Expanding a Finite Blaschke Product

( X ) and a vector x ∈ X , let σ T ( x ) denote the local spectrum of T at x . For two nonzero vectors x 0 ∈ X and y 0 ∈ Y , we show that a map ϕ from

On a conjecture about the eigenvalues of doubly stochastic matrices

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