Search

In this paper, we construct a symbol calculus yielding short exact sequences for the dual Toeplitz algebra generated by all bounded dual Toeplitz operators on the Hardy space associated with the polydisk D n in the unitary space C n , that have been introduced and well studied in our earlier paper (Benaissa and Guediri in Taiwan J Math 19: 31–49, 2015), as well as for the C*-subalgebra generated by dual Toeplitz operators with symbols continuous on the associated hypertorus T n . [ABSTRACT FROM AUTHOR]

In this paper, we study several properties of an orthonormal basis { N n (z) } for the Newton space N 2 (P) . In particular, we investigate the product of N m and N m and the orthogonal projection P of N n ‾ N m that maps from L 2 (P) onto N 2 (P) . Moreover, we find the matrix representation of Toeplitz operators with respect to such an orthonormal basis on the Newton space N 2 (P) . [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the various properties of the Toeplitz operators acting on the Dirichlet spaces. First, we consider the matrix representation of Toeplitz operators with harmonic and monomial symbols. Second, we establish the expansivity and contractivity of the Toeplitz operators T φ with monomial symbols φ . Third, we give a necessary and sufficient conditions for the normality and hyponormality of the Toeplitz operators T φ with such symbols on the Dirichlet spaces. [ABSTRACT FROM AUTHOR]

In this paper, we study Hankel operators on the doubling Fock spaces for all possible 1 ≤ p , q < ∞ . We characterize those symbols f for which the Hankel operators H f and H f ¯ are simultaneously bounded or compact from doubling Fock space F φ p to Lebesgue space L φ q , where φ is a nonzero subharmonic function such that Δ φ d A is a doubling measure. [ABSTRACT FROM AUTHOR]

In this paper, we establish an equivariant version of Dai–Zhang's Toeplitz index theorem for compact odd-dimensional spin manifolds with even-dimensional boundary. [ABSTRACT FROM AUTHOR]

The paper is devoted to weighted estimates for operators of fractional integration of variable order of Bergman type in generalized variable Hölder spaces of holomorphic functions on the unit disc D . Due to the choice of the weight, we can include in consideration the case when the real part of the complex power of the operator degenerates. We prove the estimates of Zygmund type for the modulus of continuity, and then we obtain the corresponding weighted boundedness result. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the frequent hypercyclicity of the Toeplitz operator T Φ and their tensor products on the Hardy space with the symbol of the form Φ (z) = p (1 z) + φ (z) , where p is a polynomial and φ ∈ H ∞ . We also give some sufficient conditions for T Φ 1 ⊗ T Φ 2 to be hypercyclic and construct an example such that neither T Φ 1 nor T Φ 2 is hypercyclic, but T Φ 1 ⊗ T Φ 2 is frequently hypercyclic. Moreover, we also characterize the mixing property and chaoticity of T Φ and T Φ 1 ⊗ T Φ 2 . [ABSTRACT FROM AUTHOR]

In this paper, we establish the convergence of several Galerkin–Petrov methods, including the finite section method, the polynomial collocation method and the analytic element collocation method for Toeplitz operators on Dirichlet type spaces. In particular, we show that such methods converge if the basis functions and test functions own certain circular symmetry. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we construct a symbol calculus yielding short exact sequences for the dual Toeplitz algebra generated by all bounded dual Toeplitz operators on the Hardy space associated with the polydisk $${\mathbb {D}}^n$$ D n in the unitary space $${\mathbb {C}}^n$$ C n , that have been introduced and well studied in our earlier paper (Benaissa and Guediri in Taiwan J Math 19: 31–49, 2015), as well as for the C*-subalgebra generated by dual Toeplitz operators with symbols continuous on the associated hypertorus $${\mathbb {T}}^n$$ T n .

We introduce an extended class of cross-Toeplitz operators which act between Fock–Segal–Bargmann spaces with different weights. It is natural to consider these operators in the framework of representation theory of the Heisenberg group. Our main technique is representation of cross-Toeplitz by two-sided relative convolutions from the Heisenberg group. In turn, two-sided convolutions are reduced to usual (one-sided) convolutions on the Heisenberg group of the doubled dimensionality. This allows us to utilise the powerful group-representation technique of coherent states, co- and contra-variant transforms, twisted convolutions, symplectic Fourier transform, etc. We discuss connections of (cross-)Toeplitz operators with pseudo-differential operators, localisation operators in time–frequency analysis, and characterisation of kernels in terms of ladder operators. The paper is written in a detailed and reasonably self-contained manner to be suitable as an introduction into group-theoretical methods in phase space and time–frequency operator theory. [ABSTRACT FROM AUTHOR]

In this paper, we consider the hyponormality of Toeplitz operators acting on the weighted Bergman space A α 2 (D). We establish necessary or sufficient conditions for the hyponormality of Toeplitz operators with non-harmonic symbols φ (z) that are bivariate polynomials in z and z ¯ (i.e., φ (z) = a z m z ¯ n + b z s z ¯ t ). In particular, we present some characteristics according to the coefficients and degree of φ (z). [ABSTRACT FROM AUTHOR]

We give a concrete description of complex symmetric monomial Toeplitz operators T z p z ¯ q on the weighted Bergman space A2(Ω), where Ω denotes the unit ball or the unit polydisk. We provide a necessary condition for T z p z ¯ q to be complex symmetric. When p,q ∈ ℕ2, we prove that T z p z ¯ q is complex symmetric on A2(Ω) if and only if p1 = q2 and P2 = q1. Moreover, we completely characterize when monomial Toeplitz operators T z p z ¯ q on A 2 (D n) are JU-symmetric with the n × n symmetric unitary matrix U. [ABSTRACT FROM AUTHOR]

Let μ be a finite positive measure on the unit disk and let j ⩾ 1 be an integer. D. Suárez (2015) gave some conditions for a generalized Toeplitz operator to be bounded or compact. We first give a necessary and sufficient condition for to be in the Schatten p-class for 1 ⩽ p < ∞ on the Bergman space A2, and then give a sufficient condition for to be in the Schatten p-class (0 < p < 1) on A2. We also discuss the generalized Toeplitz operators with general bounded symbols. If ϕ ∈ L∞ (D, dA) and 1 < p < ∞, we define the generalized Toeplitz operator on the Bergman space Ap and characterize the compactness of the finite sum of operators of the form . [ABSTRACT FROM AUTHOR]

We give a new algorithm for the construction of the unique superoptimal analytic approximant of a given continuous matrix‐valued function on the unit circle, using exterior powers of operators in preference to spectral or Wiener–Masani factorizations. [ABSTRACT FROM AUTHOR]