scholarly journals On unconditional exponential bases in weighted spaces on real axis

2015 ◽  
Vol 7 (3) ◽  
pp. 108-118
Author(s):  
Artur Airatovich Yunusov
Keyword(s):  
Real Axis ◽  
Weighted Spaces ◽  
Exponential Bases

On unconditional bases of exponentials in weighted spaces on an interval of the real axis

2017 ◽  
Vol 28 (5) ◽  
pp. 689-706
Author(s):  
K. P. Isaev ◽  
R. S. Yulmukhametov ◽  
A. A. Yunusov
Keyword(s):  
Real Axis ◽  
Weighted Spaces ◽  
The Real ◽  
Unconditional Bases

Completeness of exponential systems in weighted spaces on the real axis

2009 ◽  
Vol 80 (3) ◽  
pp. 810-813
Author(s):  
V. V. Napalkov ◽  
A. A. Rumyantseva ◽  
R. S. Yulmukhametov
Keyword(s):  
Real Axis ◽  
Weighted Spaces ◽  
The Real

scholarly journals On unconditional exponential bases in weak weighted spaces on segment

2016 ◽  
Vol 8 (4) ◽  
pp. 88-97
Author(s):  
Konstantin Petrovich Isaev ◽  
Anastasiya Vladimirovna Lutsenko ◽  
Rinad Salavatovich Yulmukhametov
Keyword(s):  
Weighted Spaces ◽  
Exponential Bases

Degree of best one-sided approximation by smooth multi-Dimensional spline in weighted spaces

2014 ◽  
Vol 1 (3) ◽  
pp. 87-95
Author(s):  
Jawad Judy ◽  
◽  
Saheb AL-Saidy
Keyword(s):  
Weighted Spaces

scholarly journals Semi-Exponential Operators

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 637
Author(s):  
Monika Herzog
Keyword(s):  
Exponential Type ◽  
Probabilistic Approach ◽  
Weighted Spaces ◽  
Approximation Properties

In this paper we study approximation properties of exponential-type operators for functions from exponential weighted spaces. We focus on some modifications of these operators and we derive a new example of such operators. A probabilistic approach for these modifications is also demonstrated.

scholarly journals The Complexity of Approximating the Matching Polynomial in the Complex Plane

2021 ◽  
Vol 13 (2) ◽  
pp. 1-37
Author(s):  
Ivona Bezáková ◽  
Andreas Galanis ◽  
Leslie Ann Goldberg ◽  
Daniel Štefankovič
Keyword(s):  
Real Axis ◽  
Complex Plane ◽  
Maximum Degree ◽  
Negative Real Axis ◽  
Positive Real ◽  
Bounded Degree ◽  
Matching Polynomial ◽  
Correlation Decay ◽  
Connective Constant ◽  
General Complex

We study the problem of approximating the value of the matching polynomial on graphs with edge parameter γ, where γ takes arbitrary values in the complex plane. When γ is a positive real, Jerrum and Sinclair showed that the problem admits an FPRAS on general graphs. For general complex values of γ, Patel and Regts, building on methods developed by Barvinok, showed that the problem admits an FPTAS on graphs of maximum degree Δ as long as γ is not a negative real number less than or equal to −1/(4(Δ −1)). Our first main result completes the picture for the approximability of the matching polynomial on bounded degree graphs. We show that for all Δ ≥ 3 and all real γ less than −1/(4(Δ −1)), the problem of approximating the value of the matching polynomial on graphs of maximum degree Δ with edge parameter γ is #P-hard. We then explore whether the maximum degree parameter can be replaced by the connective constant. Sinclair et al. showed that for positive real γ, it is possible to approximate the value of the matching polynomial using a correlation decay algorithm on graphs with bounded connective constant (and potentially unbounded maximum degree). We first show that this result does not extend in general in the complex plane; in particular, the problem is #P-hard on graphs with bounded connective constant for a dense set of γ values on the negative real axis. Nevertheless, we show that the result does extend for any complex value γ that does not lie on the negative real axis. Our analysis accounts for complex values of γ using geodesic distances in the complex plane in the metric defined by an appropriate density function.

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