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Berezin and Berezin-Toeplitz quantizations for general function spaces.

Miroslav Englis (2006)

Revista Matemática Complutense

The standard Berezin and Berezin-Toeplitz quantizations on a Kähler manifold are based on operator symbols and on Toeplitz operators, respectively, on weighted L2-spaces of holomorphic functions (weighted Bergman spaces). In both cases, the construction basically uses only the fact that these spaces have a reproducing kernel. We explore the possibilities of using other function spaces with reproducing kernels instead, such as L2-spaces of harmonic functions, Sobolev spaces, Sobolev spaces of holomorphic...

Bergelson's theorem for weakly mixing C*-dynamical systems

Rocco Duvenhage (2009)

Studia Mathematica

We study a nonconventional ergodic average for asymptotically abelian weakly mixing C*-dynamical systems, related to a second iteration of Khinchin's recurrence theorem obtained by Bergelson in the measure-theoretic case. A noncommutative recurrence theorem for such systems is obtained as a corollary.

Bernstein inequality for the parameter of the pth order autoregressive process AR(p)

Samir Benaissa (2006)

Applicationes Mathematicae

The autoregressive process takes an important part in predicting problems leading to decision making. In practice, we use the least squares method to estimate the parameter θ̃ of the first-order autoregressive process taking values in a real separable Banach space B (ARB(1)), if it satisfies the following relation: X ̃ t = θ ̃ X ̃ t - 1 + ε ̃ t . In this paper we study the convergence in distribution of the linear operator I ( θ ̃ T , θ ̃ ) = ( θ ̃ T - θ ̃ ) θ ̃ T - 2 for ||θ̃|| > 1 and so we construct inequalities of Bernstein type for this operator.

Besov spaces and 2-summing operators

M. A. Fugarolas (2004)

Colloquium Mathematicae

Let Π₂ be the operator ideal of all absolutely 2-summing operators and let I m be the identity map of the m-dimensional linear space. We first establish upper estimates for some mixing norms of I m . Employing these estimates, we study the embedding operators between Besov function spaces as mixing operators. The result obtained is applied to give sufficient conditions under which certain kinds of integral operators, acting on a Besov function space, belong to Π₂; in this context, we also consider the...

Besov spaces and function series on Lie groups

Leszek Skrzypczak (1993)

Commentationes Mathematicae Universitatis Carolinae

In the paper we investigate the absolute convergence in the sup-norm of Harish-Chandra's Fourier series of functions belonging to Besov spaces defined on non-compact connected Lie groups.

Besov spaces and function series on Lie groups (II).

Leszek Skrzypczak (1993)

Collectanea Mathematica

In this paper we investigate the absolute convergence in the sup-norm of two-sided Harish-Chandra's Fourier series of functions belonging to Zygmund-Hölder spaces defined on non-compact connected Lie groups.[Part I of the article in MR1240211].

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