Stein Spaces M for which O(M) is Isomorphic to a Power Series Space

1989 ◽  
pp. 115-154 ◽  
Author(s):  
Aydin Aytuna
Keyword(s):  
Power Series ◽  
Power Series Space ◽  
Series Space

scholarly journals DUALITY FOR SOME LARGE SPACES OF ANALYTIC FUNCTIONS

2001 ◽  
Vol 44 (3) ◽  
pp. 571-583 ◽  
Author(s):  
H. Jarchow ◽  
V. Montesinos ◽  
K. J. Wirths ◽  
J. Xiao
Keyword(s):  
Power Series ◽  
Analytic Functions ◽  
Nuclear Power ◽  
Orlicz Spaces ◽  
Primary 46E10 ◽  
Smirnov Class ◽  
Power Series Space ◽  
Secondary 30D55 ◽  
Series Space ◽  
Spaces Of Analytic Functions

AbstractWe characterize the duals and biduals of the $L^p$-analogues $\mathcal{N}_\alpha^p$ of the standard Nevanlinna classes $\mathcal{N}_\alpha$, $\alpha\ge-1$ and $1\le p\lt \infty$. We adopt the convention to take $\mathcal{N}_{-1}^p$ to be the classical Smirnov class $\mathcal{N}^+$ for $p=1$, and the Hardy–Orlicz space $LH^p$ $(=(\text{Log}^+H)^p)$ for $1\lt p\lt\infty$. Our results generalize and unify earlier characterizations obtained by Eoff for $\alpha=0$ and $\alpha=-1$, and by Yanigahara for the Smirnov class.Each $\mathcal{N}_\alpha^p$ is a complete metrizable topological vector space (in fact, even an algebra); it fails to be locally bounded and locally convex but admits a separating dual. Its bidual will be identified with a specific nuclear power series space of finite type; this turns out to be the ‘Fréchet envelope’ of $\mathcal{N}_\alpha^p$ as well.The generating sequence of this power series space is of the form $(n^\theta)_{n\in\mathbb{N}}$ for some $0\lt\theta\lt1$. For example, the $\theta$s in the interval $(\smfr12,1)$ correspond in a bijective fashion to the Nevanlinna classes $\mathcal{N}_\alpha$, $\alpha\gt-1$, whereas the $\theta$s in the interval $(0,\smfr12)$ correspond bijectively to the Hardy–Orlicz spaces $LH^p$, $1\lt p\lt \infty$. By the work of Yanagihara, $\theta=\smfr12$ corresponds to $\mathcal{N}^+$.As in the work by Yanagihara, we derive our results from characterizations of coefficient multipliers from $\mathcal{N}_\alpha^p$ into various smaller classical spaces of analytic functions on $\Delta$.AMS 2000 Mathematics subject classification: Primary 46E10; 46A11; 47B38. Secondary 30D55; 46A45; 46E15\vskip-3pt

On Complemented Subspaces of Non-Archimedean Power Series Spaces

2011 ◽  
Vol 63 (5) ◽  
pp. 1188-1200 ◽  
Author(s):  
Wiesław Śliwa ◽  
Agnieszka Ziemkowska
Keyword(s):  
Power Series ◽  
Double Sequence ◽  
Schauder Basis ◽  
Fréchet Spaces ◽  
Continuous Linear ◽  
Linear Map ◽  
Complemented Subspaces ◽  
Complemented Subspace ◽  
Power Series Space ◽  
Series Space

Abstract The non-archimedean power series spaces, A1(a) and A∞(b), are the best known and most important examples of non-archimedean nuclear Fréchet spaces. We prove that the range of every continuous linear map from Ap(a) to Aq(b) has a Schauder basis if either p = 1 or p = ∞ and the set Mb,a of all bounded limit points of the double sequence (bi/aj )i, j∈ℕ is bounded. It follows that every complemented subspace of a power series space Ap(a) has a Schauder basis if either p = 1 or p = ∞ and the set Ma,a is bounded.

scholarly journals Basis sequences in a stable finite type power series space

1980 ◽  
Vol 68 (2) ◽  
pp. 117-130 ◽  
Author(s):  
Ed Dubinsky
Keyword(s):  
Power Series ◽  
Finite Type ◽  
Power Series Space ◽  
Series Space ◽  
Type Power

scholarly journals A Generalization of Caristi’s Fixed Point Theorem in the Variable Exponent Weighted Formal Power Series Space

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Awad A. Bakery ◽  
M. H. El Dewaik
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Power Series ◽  
Formal Power Series ◽  
Point Theorem ◽  
Entire Functions ◽  
Caristi’S Fixed Point Theorem ◽  
Series Space ◽  
Formal Power ◽  
Caristi's Fixed Point Theorem

Suppose p n be sequence of positive reals. By H w p n , we represent the space of all formal power series ∑ n = 0 ∞ a n z n equipped with ∑ n = 0 ∞ λ a n / n + 1 p n < ∞ , for some λ > 0 . Various topological and geometric behavior of H w p n and the prequasi ideal constructs by s -numbers and H w p n have been considered. The upper bounds for s -numbers of infinite series of the weighted n -th power forward shift operator on H w p n with applications to some entire functions are granted. Moreover, we investigate an extrapolation of Caristi’s fixed point theorem in H w p n .

scholarly journals The Spectrum of Mapping Ideals of Type Variable Exponent Function Space of Complex Variables with Some Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Awad A. Bakery ◽  
Mustafa M. Mohammed
Keyword(s):  
Function Space ◽  
Variable Exponent ◽  
Entire Functions ◽  
Shift Operator ◽  
Complex Variables ◽  
Power Series Space ◽  
Series Space ◽  
Backward Shift ◽  
Type Variable ◽  
Formal Power

The topological and geometric behaviors of the variable exponent formal power series space, as well as the prequasi-ideal construction by s -numbers and this function space of complex variables, are investigated in this article. Upper bounds for s -numbers of infinite series of the weighted n th power forward and backward shift operator on this function space are being investigated, with applications to some entire functions.

The Software «MMI–calibration 3.0»

Metrologiya ◽  
2020 ◽  
pp. 16-24
Author(s):  
Alexandr D. Chikmarev
Keyword(s):  
Power Series ◽  
Data Processing ◽  
Statistical Treatment ◽  
Correction Function ◽  
Calibration Function ◽  
Measuring Instrument ◽  
Working Standard ◽  
Calibration Protocol ◽  
Error Probabilities ◽  
Continuous Power

A single program has been developed to ensure that the final result of the data processing of the measurement calibration protocol is obtained under normal conditions. The calibration result contains a calibration function or a correction function in the form of a continuous sedate series and a calibration chart based on typical additive error probabilities. Solved the problem of the statistical treatment of the calibration protocol measuring in normal conditions within a single program “MMI–calibration 3.0” that includes identification of the calibration function in a continuous power series of indications of a measuring instrument and chart calibration. An example of solving the problem of calibration of the thermometer by the working standard of the 3rd grade with the help of the “MMI-calibration 3.0” program.

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