Browsing by Author "Astaburuaga, M. A."

Now showing 1 - 5 of 5
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    Absence of point spectrum for unitary operators
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2008) Astaburuaga, M. A.; Bourget, O.; Cortes, V. H.; Fernandez, C.
    Let us consider the time-dependent Schrodinger equation,
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    Extremal values of the sojourn time
    (2010) Astaburuaga, M. A.; Cortes, V. H.; Duclos, P.
    Consider a self-adjoint operator H on a separable Hilbert space H with non-trivial absolutely continuous component. We study the general properties of the real-valued functional, tau(H) (psi) = f(R) vertical bar(e(-itH)psi, psi)vertical bar(2) dt, which in quantum mechanics represents the sojourn time (or life time) of an initial state psi is an element of H. We characterize the critical points of the sojourn time, tau(X), of the operator multiplication by x in L(2)(R), and prove that it attains a global maximum in the unit sphere of the Sobolev space W(1,2)(R).
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    Floquet operators without singular continuous spectrum
    (2006) Astaburuaga, M. A.; Bourget, O.; Cortes, V. H.; Fernandez, C.
    Let U be a unitary operator defined on a infinite-dimensional separable complex Hilbert space R. Assume there exists a self-adjoint operator A on R such that
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    Singular rank one perturbations
    (2022) Astaburuaga, M. A.; Cortes, V. H.; Fernandez, C.; Del Rio, R.
    In this paper, A = B + V represents a self-adjoint operator acting on a Hilbert space H. We set a general theoretical framework and obtain several results for singular perturbations of A of the type A(beta) = A + beta tau*tau for tau being a functional defined in a subspace of H. In particular, we apply these results to H-beta = -Delta + V + beta|delta >
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    Spectral properties for perturbations of unitary operators
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2011) Astaburuaga, M. A.; Cortes, V. H.
    Consider a unitary operator U-0 acting on a complex separable Hilbert space H. In this paper we study spectral properties for perturbations of U-0 of the type,