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Biseparating maps on generalized Lipschitz spaces

Denny H. Leung (2010)

Studia Mathematica

Let X, Y be complete metric spaces and E, F be Banach spaces. A bijective linear operator from a space of E-valued functions on X to a space of F-valued functions on Y is said to be biseparating if f and g are disjoint if and only if Tf and Tg are disjoint. We introduce the class of generalized Lipschitz spaces, which includes as special cases the classes of Lipschitz, little Lipschitz and uniformly continuous functions. Linear biseparating maps between generalized Lipschitz spaces are characterized...

Bloch-to-Hardy composition operators

Evgueni Doubtsov, Andrei Petrov (2013)

Open Mathematics

Let φ be a holomorphic mapping between complex unit balls. We characterize those regular φ for which the composition operators C φ: f ↦ f ○ φ map the Bloch space into the Hardy space.

Boundary feedback stabilization of a three-layer sandwich beam : Riesz basis approach

Jun-Min Wang, Bao-Zhu Guo, Boumediène Chentouf (2006)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we consider the boundary stabilization of a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop system are concluded. Finally, the well-posedness and regularity in the sense of Salamon-Weiss class as...

Boundary feedback stabilization of a three-layer sandwich beam: Riesz basis approach

Jun-Min Wang, Bao-Zhu Guo, Boumediène Chentouf (2005)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we consider the boundary stabilization of a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop system are concluded. Finally, the well-posedness and regularity in the sense of Salamon-Weiss class as...

Boundary vs. interior conditions associated with weighted composition operators

Kei Izuchi, Yuko Izuchi, Shûichi Ohno (2014)

Open Mathematics

Associated with some properties of weighted composition operators on the spaces of bounded harmonic and analytic functions on the open unit disk 𝔻 , we obtain conditions in terms of behavior of weight functions and analytic self-maps on the interior 𝔻 and on the boundary 𝔻 respectively. We give direct proofs of the equivalence of these interior and boundary conditions. Furthermore we give another proof of the estimate for the essential norm of the difference of weighted composition operators.

Bounded operators on weighted spaces of holomorphic functions on the upper half-plane

Mohammad Ali Ardalani, Wolfgang Lusky (2012)

Studia Mathematica

Let v be a standard weight on the upper half-plane , i.e. v: → ]0,∞[ is continuous and satisfies v(w) = v(i Im w), w ∈ , v(it) ≥ v(is) if t ≥ s > 0 and l i m t 0 v ( i t ) = 0 . Put v₁(w) = Im wv(w), w ∈ . We characterize boundedness and surjectivity of the differentiation operator D: Hv() → Hv₁(). For example we show that D is bounded if and only if v is at most of moderate growth. We also study composition operators on Hv().

Bounded Toeplitz and Hankel products on weighted Bergman spaces of the unit ball

Małgorzata Michalska, Maria Nowak, Paweł Sobolewski (2010)

Annales Polonici Mathematici

We prove a sufficient condition for products of Toeplitz operators T f T , where f,g are square integrable holomorphic functions in the unit ball in ℂⁿ, to be bounded on the weighted Bergman space. This condition slightly improves the result obtained by K. Stroethoff and D. Zheng. The analogous condition for boundedness of products of Hankel operators H f H * g is also given.

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