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On the periodicity of trigonometric functions generalized to quotient rings of R[x]

Claude Gauthier (2006)

Open Mathematics

We apply a method of Euler to algebraic extensions of sets of numbers with compound additive inverse which can be seen as quotient rings of R[x]. This allows us to evaluate a generalization of Riemann’s zeta function in terms of the period of a function which generalizes the function sin z. It follows that the functions generalizing the trigonometric functions on these sets of numbers are not periodic.

On the powers of quasihomogeneous Toeplitz operators

Aissa Bouhali, Zohra Bendaoud, Issam Louhichi (2021)

Czechoslovak Mathematical Journal

We present sufficient conditions for the existence of p th powers of a quasihomogeneous Toeplitz operator T e i s θ ψ , where ψ is a radial polynomial function and p , s are natural numbers. A large class of examples is provided to illustrate our results. To our best knowledge those examples are not covered by the current literature. The main tools in the proof of our results are the Mellin transform and some classical theorems of complex analysis.

On the Product of Functions in BMO and H 1

Aline Bonami, Tadeusz Iwaniec, Peter Jones, Michel Zinsmeister (2007)

Annales de l’institut Fourier

The point-wise product of a function of bounded mean oscillation with a function of the Hardy space H 1 is not locally integrable in general. However, in view of the duality between H 1 and B M O , we are able to give a meaning to the product as a Schwartz distribution. Moreover, this distribution can be written as the sum of an integrable function and a distribution in some adapted Hardy-Orlicz space. When dealing with holomorphic functions in the unit disc, the converse is also valid: every holomorphic...

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