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A Class of Contractions in Hilbert Space and Applications

Nick Dungey (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

We characterize the bounded linear operators T in Hilbert space which satisfy T = βI + (1-β)S where β ∈ (0,1) and S is a contraction. The characterizations include a quadratic form inequality, and a domination condition of the discrete semigroup ( T ) n = 1 , 2 , . . . by the continuous semigroup ( e - t ( I - T ) ) t 0 . Moreover, we give a stronger quadratic form inequality which ensures that s u p n T - T n + 1 : n = 1 , 2 , . . . < . The results apply to large classes of Markov operators on countable spaces or on locally compact groups.

A class of pairs of weights related to the boundedness of the Fractional Integral Operator between L p and Lipschitz spaces

Gladis Pradolini (2001)

Commentationes Mathematicae Universitatis Carolinae

In [P] we characterize the pairs of weights for which the fractional integral operator I γ of order γ from a weighted Lebesgue space into a suitable weighted B M O and Lipschitz integral space is bounded. In this paper we consider other weighted Lipschitz integral spaces that contain those defined in [P], and we obtain results on pairs of weights related to the boundedness of I γ acting from weighted Lebesgue spaces into these spaces. Also, we study the properties of those classes of weights and compare...

A class of singular fourth-order boundary value problems with nonhomogeneous nonlinearity

Qingliu Yao (2013)

Annales Polonici Mathematici

We study the existence of positive solutions to a class of singular nonlinear fourth-order boundary value problems in which the nonlinearity may lack homogeneity. By introducing suitable control functions and applying cone expansion and cone compression, we prove three existence theorems. Our main results improve the existence result in [Z. L. Wei, Appl. Math. Comput. 153 (2004), 865-884] where the nonlinearity has a certain homogeneity.

A class of tridiagonal operators associated to some subshifts

Christian Hernández-Becerra, Benjamín A. Itzá-Ortiz (2016)

Open Mathematics

We consider a class of tridiagonal operators induced by not necessary pseudoergodic biinfinite sequences. Using only elementary techniques we prove that the numerical range of such operators is contained in the convex hull of the union of the numerical ranges of the operators corresponding to the constant biinfinite sequences; whilst the other inclusion is shown to hold when the constant sequences belong to the subshift generated by the given biinfinite sequence. Applying recent results by S. N....

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