On extended eigenvalues and extended eigenvectors of some operator classes

Description of extended eigenvalues and extended eigenvectors of integration operators on the Wiener algebra

In the present paper we consider the Volterra integration operator V on the Wiener algebra W (D) of analytic functions on the unit discD of the complex plane C. A complex number is called an extended eigenvalue of V if there exists a nonzero operator A satisfying the equation AV = V A. We prove that the set of all extended eigenvalues of V is precisely the set C\{0}, and describe in terms of Du...

On the Extended Eigenvalues of Some Volterra Operators

On Extended Eigenvalues of Operators

A complex number λ is an extended eigenvalue of an operator A if there is a nonzero operator X such that AX = λXA. We characterize the the set of extended eigenvalues for operators acting on finite dimensional spaces, finite rank operators, Jordan blocks, and C0 contractions. We also describe the relationship between the extended eigenvalues of an operator A and its powers. We derive some appli...

Some properties of extended multiplier transformations to the classes of meromorphic multivalent functions

 In this paper, we introduce new classes $sum_{k,p,n}(alpha ,m,lambda ,l,rho )$ and $mathcal{T}_{k,p,n}(alpha ,m,lambda ,l,rho )$ of p-valent meromorphic functions defined by using the extended multiplier transformation operator. We use a strong convolution technique and derive inclusion results. A radius problem and some other interesting properties of these classes are discussed.

Notes on Eigenvalues and Eigenvectors

Exercise 4. Let λ be an eigenvalue of A and let Eλ(A) = {x ∈ C|Ax = λx} denote the set of all eigenvectors of A associated with λ (including the zero vector, which is not really considered an eigenvector). Show that this set is a (nontrivial) subspace of C. Definition 5. Given A ∈ Cm×m, the function pm(λ) = det(λI − A) is a polynomial of degree at most m. This polynomial is called the character...