Ultrapolynomial
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In mathematics, an ultrapolynomial is a power series in several variables whose coefficients are bounded in some specific sense.
Definition
Let and a field (typically or ) equipped with a norm (typically the absolute value). Then a function of the form is called an ultrapolynomial of class , if the coefficients satisfy for all , for some and (resp. for every and some ).
References
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- {{cite arXiv |last1=Lozanov-Crvenković |first1=Z. |last2=Perišić |first2=D. |eprint=math/0702093 |title=Kernel theorem for the space of Beurling - Komatsu tempered ultradistibutions |class= |date=5 Feb 2007 }}
- {{cite journal |author=Lozanov-Crvenković, Z |title= Kernel theorems for the spaces of tempered ultradistributions |journal= Integral Transforms and Special Functions |pages=699–713 |date=October 2007 |volume= 18 |issue= 10 |doi=10.1080/10652460701445658|s2cid= 123420666 }}
- {{cite journal |last1=Pilipović |first1=Stevan |last2=Pilipović |first2=Bojan |last3=Prangoski |first3=Jasson |arxiv=1711.05628 |title=Infinite order $$\Psi $$DOs: Composition with entire functions, new Shubin-Sobolev spaces, and index theorem |journal=Analysis and Mathematical Physics |year=2021 |volume=11 |issue=3 |doi=10.1007/s13324-021-00545-w |s2cid=201107206 }}
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