Displaying similar documents to “Interpolation of entire functions on regular sparse sets and q -Taylor series”

The deficiency of entire functions with Fejér gaps

Takafumi Murai (1983)

Annales de l'institut Fourier

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We say that an entire function f ( z ) = ∑ k = 0 a k z n k ( 0 = n 0 < n 1 < n 2 < ... ) has Fejér gaps if ∑ k = 1 ∞ 1 / n k < ∞ . The main result of this paper is as follows: An entire function with Fejér gaps has no finite deficient value.

On approximation and interpolation of entire functions with index-pair (p,q).

H. S. Kasana, Devendra Kumar (1994)

Publicacions Matemàtiques

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In this paper we have studied the Chebyshev and interpolation errors for functions in C(E), the normed algebra of analytic functions on a compact set E of positive transfinite diameter. The (p,q)-order and generalized (p,q)-type have been characterized in terms of these approximation errors. Finally, we have obtained a saturation theorem for f ∈ C(E) which can be extended to an entire function of (p,q)-order 0 or 1 and for entire functions of minimal generalized (p,q)-type.