Singularities of carleman type for subsystems of a trigonometric system

S. F. Lukomskii

doi:10.1007/bf01095117

Singularities of carleman type for subsystems of a trigonometric system

Mathematical Notes ◽

10.1007/bf01095117 ◽

1974 ◽

Vol 15 (4) ◽

pp. 301-304

Author(s):

S. F. Lukomskii

Keyword(s):

Trigonometric System ◽

Carleman Type

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Convergence of greedy approximation for the trigonometric system

Analysis Mathematica ◽

10.1007/s10476-005-0007-0 ◽

2005 ◽

Vol 31 (2) ◽

pp. 85-115 ◽

Cited By ~ 2

Author(s):

S. V. Konyagin ◽

V. N. Temlyakov

Keyword(s):

Trigonometric System ◽

Greedy Approximation

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On Parseval’s equality for rearrangements of the trigonometric system

Mathematical Notes ◽

10.1134/s0001434611110186 ◽

2011 ◽

Vol 90 (5-6) ◽

pp. 780-783

Author(s):

A. I. Rubinshtein

Keyword(s):

Trigonometric System ◽

Parseval’S Equality

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Vector and operator-valued holomorphic functions representable by Carleman type formulas

Complex Variables Theory and Application An International Journal ◽

10.1080/02781070412331327883 ◽

2004 ◽

Vol 49 (15) ◽

pp. 1117-1128 ◽

Cited By ~ 1

Author(s):

George Chailos

Keyword(s):

Holomorphic Functions ◽

Carleman Type

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Three-Element Problem of Carleman Type for Bianalitic Functions in a Circle

Izvestiya of Saratov University New Series Series Mathematics Mechanics Informatics ◽

10.18500/1816-9791-2012-12-2-18-26 ◽

2012 ◽

Vol 12 (2) ◽

pp. 18-26 ◽

Cited By ~ 1

Author(s):

Natal’ya Romanovna Perelman ◽

◽

Karim Magomedovich Rasulov ◽

Keyword(s):

Carleman Type

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Approximation formulas for the constant e and an improvement to a Carleman-type inequality

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2018.06.011 ◽

2018 ◽

Vol 466 (1) ◽

pp. 711-725

Author(s):

Chao-Ping Chen ◽

Richard B. Paris

Keyword(s):

Type Inequality ◽

Constant E ◽

Approximation Formulas ◽

Carleman Type

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Analysis of chaotic characteristics of trigonometric function system

Modern Physics Letters B ◽

10.1142/s0217984920502103 ◽

2020 ◽

Vol 34 (21) ◽

pp. 2050210

Author(s):

Wanbo Yu ◽

Ting Yu

Keyword(s):

Social Sciences ◽

Dynamic System ◽

Necessary Conditions ◽

Fluid Motion ◽

Nonlinear Dynamic System ◽

Chaotic Sequence ◽

Trigonometric System ◽

Secure Communications ◽

Key Space ◽

Mathematical Derivation

Chaos, as an important subject of nonlinear science, plays an important role in solving problems in both natural sciences and social sciences such as the fields of secure communications, fluid motion, particle motion and so on. Aiming at this problem, this paper proposes a nonlinear dynamic system composed of product trigonometric functions and studies its chaotic characteristics. Through the mathematical derivation of the system’s period, the analysis of the necessary conditions at the fixed point, the experimental drawing of the Lyapunov exponential graph and the branch graph of the system, it is proved that the system has larger chaotic interval and stronger chaotic characteristics. The parameters of the proposed dynamic system are generated randomly, and then the chaotic sequence can be generated. The chaotic sequence is used to encrypt the digital image, a good encryption effect is obtained, and there is a large key space. At the same time, the motion of the particles in the space magnetic field is simulated, which further proves that the trigonometric system has strong chaotic characteristics.

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