On generalized definitions of ultradifferentiable classes

Abstract

We show that the ultradifferentiable-like classes of smooth functions introduced and studied by S. Pilipović, N. Teofanov and F. Tomić are special cases of the general framework of spaces of ultradifferentiable functions defined in terms of weight matrices in the sense of A. Rainer and the third author. We study classes "beyond geometric growth factors" defined in terms of a weight sequence and an exponent sequence, prove that these new types admit a weight matrix representation and transfer known results from the matrix-type to such a non-standard ultradifferentiable setting.

Some typos corrected; to appear in Journal of Mathematical Analysis and Applications

References in corpus (3)

• The Borel map in the mixed Beurling setting
• On optimal solutions of the Borel problem in the Roumieu case
• Nonlinear conditions for ultradifferentiability: a uniform approach

Cited by in corpus (9)

• On inclusion relations between weighted spaces of entire functions
• On strong growth conditions for weighted spaces of entire functions
• Ultradifferentiable classes of entire functions
• On inclusion relations of weighted $L^p$-type spaces defined in terms of weight function matrices
• On the class of almost subadditive weight functions
• Construction of the log-convex minorant of a sequence $\{M_{\alpha }{\}}_{\alpha \in {\mathbb{N}}_0^d}$
• Surjectivity of the asymptotic Borel map in Carleman ultraholomorphic classes defined by sequences with shifted moments
• On Orlicz classes defined in terms of associated weight functions
• Gelfand-Shilov spaces for extended Gevrey regularity