2021-12-17
AUTHORSBoban Karapetrović, Javad Mashreghi
ABSTRACTWe explore the relation between Hadamard products of two entire functions in the weighted Fock space Fγp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {F}^p_\gamma $$\end{document} and their integral Gaussian means. By introducing the key auxiliary function κγ,r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa _{\gamma ,r}$$\end{document}, we show that the growth of the Gaussian means of the Hadamard product f∗g∗κγ,r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f*g*\kappa _{\gamma ,r}$$\end{document} is controlled by the growth of Gaussian means of f and g. Among several consequences of this observation, in particular, we establish the sub-multiplicative property f∗g∗κF1≤‖f‖F1‖g‖F1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\| f*g*\kappa \right\| _{\mathrm {F}^1}\le \Vert f\Vert _{\mathrm {F}^1}\Vert g\Vert _{\mathrm {F}^1}$$\end{document} for functions in the classical Fock space F1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {F}^1$$\end{document}. More... »
PAGES51
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
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