Complemented infinite type power series subspaces of nuclear Fréchet spaces

1989 ◽  
Vol 283 (2) ◽  
pp. 193-202 ◽  
Author(s):  
A. Aytuna ◽  
J. Krone ◽  
T. Terzioğlu
Keyword(s):  
Power Series ◽  
Fréchet Spaces ◽  
Infinite Type ◽  
Type Power

Integral expressions for Mathieu-type power series and for the Butzer-Flocke-Hauss Ω-function

2011 ◽  
Vol 14 (4) ◽  
Author(s):  
Živorad Tomovski ◽  
Tibor Pogány
Keyword(s):  
Power Series ◽  
Fractional Order ◽  
Integral Representations ◽  
Type Power

AbstractIn this paper several integral representations for the generalized fractional order Mathieu type power series $S_\mu (r;x) = \sum\limits_{n = 1}^\infty {\frac{{2nx^n }} {{(n^2 + r^2 )^{\mu + 1} }}(r \in \mathbb{R},\mu > 0,|x| \leqslant 1)} $ are presented. Also new integral expressions are derived for the Butzer-Flocke-Hauss (BFH) complete Omega function.

scholarly journals Power series expansions of modular forms and p-adic interpolation of the square roots of Rankin–Selberg special values

2021 ◽  
pp. 1-41
Author(s):  
Andrea Mori
Keyword(s):  
Power Series ◽  
Modular Forms ◽  
Level Structure ◽  
Automorphic Representation ◽  
Base Change ◽  
Series Expansions ◽  
Square Roots ◽  
Infinite Type ◽  
Special Values ◽  
Power Series Expansions

Let [Formula: see text] be a newform of even weight [Formula: see text] for [Formula: see text], where [Formula: see text] is a possibly split indefinite quaternion algebra over [Formula: see text]. Let [Formula: see text] be a quadratic imaginary field splitting [Formula: see text] and [Formula: see text] an odd prime split in [Formula: see text]. We extend our theory of [Formula: see text]-adic measures attached to the power series expansions of [Formula: see text] around the Galois orbit of the CM point corresponding to an embedding [Formula: see text] to forms with any nebentypus and to [Formula: see text] dividing the level of [Formula: see text]. For the latter we restrict our considerations to CM points corresponding to test objects endowed with an arithmetic [Formula: see text]-level structure. Also, we restrict these [Formula: see text]-adic measures to [Formula: see text] and compute the corresponding Euler factor in the formula for the [Formula: see text]-adic interpolation of the “square roots”of the Rankin–Selberg special values [Formula: see text], where [Formula: see text] is the base change to [Formula: see text] of the automorphic representation of [Formula: see text] associated, up to Jacquet-Langland correspondence, to [Formula: see text] and [Formula: see text] is a compatible family of grössencharacters of [Formula: see text] with infinite type [Formula: see text].

scholarly journals The Abel-type transformations intoℓ

1999 ◽  
Vol 22 (4) ◽  
pp. 775-784
Author(s):  
Mulatu Lemma
Keyword(s):  
Power Series ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Variant ◽  
Series Method ◽  
Power Series Method ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
Type Power

Lettbe a sequence in(0,1)that converges to1, and define the Abel-type matrixAα,tbyank=(k+α     k)tnk+1(1−tn)α+1forα>−1. The matrixAα,tdetermines a sequence-to-sequence variant of the Abel-type power series method of summability introduced by Borwein in [1]. The purpose of this paper is to study these matrices as mappings intoℓ. Necessary and sufficient conditions forAα,tto beℓ-ℓ,G-ℓ, andGw-ℓare established. Also, the strength ofAα,tin theℓ-ℓsetting is investigated.

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