A spectral mapping theorem for perturbed Ornstein–Uhlenbeck operators on L2(Rd)

A note on spectral mapping theorem

This paper aims to present the well-known spectral mapping theorem for multi-variable functions.

Remarks on the inverse spectral theory for singularly perturbed operators

Let A be an unbounded from above self-adjoint operator in a separable Hilbert space H and EA(·) its spectral measure. We discuss the inverse spectral problem for singular perturbations à of A (à and A coincide on a dense set in H). We show that for any a ∈ R there exists a singular perturbation à of A such that à and A coincide in the subspace EA((−∞, a))H and simultaneously à has an additional...

On Inverse Spectral Theory for Singularly Perturbed Operators: Point Spectrum

Spectral Theorem for Self-adjoint Linear Operators

Let V be a finite-dimensional vector space, either real or complex, and equipped with an inner product 〈· , ·〉. Let A : V → V be a linear operator. Recall that the adjoint of A is the linear operator A : V → V characterized by 〈Av, w〉 = 〈v, Aw〉 ∀v, w ∈ V (0.1) A is called self-adjoint (or Hermitian) when A = A. Spectral Theorem. If A is self-adjoint then there is an orthonormal basis (o.n.b.) o...

Spectral Theorem for Normal Operators: Applications

In these notes, we present a number of interesting and diverse applications of the Spectral Theorem for Normal Operators. These include a Spectral Mapping Theorem for Normals Operators, a Spectral Characterization of Algebraic Operators, von Neumann’s Mean Ergodic Theorem, Pathconnectivity of the Group of Invertible Operators, and some Polynomial Approximation Results for Operators.