On a Max-Plus Version of the Stieltjes Function

2010 ◽  
Author(s):  
Atsushi Mukaihira ◽  
Yuya Mori ◽  
Koichi Kondo ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Stieltjes Function

scholarly journals Non-Debye Relaxations: Two Types of Memories and Their Stieltjes Character

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 477
Author(s):  
Katarzyna Górska ◽  
Andrzej Horzela
Keyword(s):  
Stochastic Processes ◽  
Spectral Function ◽  
Evolution Equations ◽  
Memory Function ◽  
Relaxation Phenomena ◽  
Stieltjes Function ◽  
Infinitely Divisible ◽  
Spectral Functions ◽  
Debye Relaxation ◽  
Relaxation Functions

In this paper, we show that spectral functions relevant for commonly used models of the non-Debye relaxation are related to the Stieltjes functions supported on the positive semi-axis. Using only this property, it can be shown that the response and relaxation functions are non-negative. They are connected to each other and obey the time evolution provided by integral equations involving the memory function M(t), which is the Stieltjes function as well. This fact is also due to the Stieltjes character of the spectral function. Stochastic processes-based approach to the relaxation phenomena gives the possibility to identify the memory function M(t) with the Laplace (Lévy) exponent of some infinitely divisible stochastic processes and to introduce its partner memory k(t). Both memories are related by the Sonine equation and lead to equivalent evolution equations which may be freely interchanged in dependence of our knowledge on memories governing the process.

The Stieltjes Function--Definition and Properties

1988 ◽  
Vol 51 (183) ◽  
pp. 281
Author(s):  
Jan Bohman ◽  
Carl-Erik Froberg
Keyword(s):  
Stieltjes Function ◽  
Function Definition

On associated and co-recursive d-orthogonal polynomials

2013 ◽  
Vol 63 (5) ◽  
Author(s):  
A. Sadek Saib ◽  
Ebtissem Zerouki
Keyword(s):  
Orthogonal Polynomials ◽  
Recurrence Relation ◽  
Explicit Form ◽  
Stieltjes Function ◽  
Stieltjes Functions ◽  
Definition Of ◽  
Dual Sequence

AbstractThe associated sequence of order r for a given d-OPS (i.e. a sequence of orthogonal polynomials satisfying a (d + 1)-order recurrence relation), is again a d-OPS. In this paper we are interested in the determination of the corresponding dual sequence. The explicit form of the dual sequence of the first associated sequence and the corresponding formal Stieltjes function are given. Indeed, we construct by recurrence the dual sequence of the r-associated sequence and we give some properties of the corresponding Stieltjes function. Second, we give the definition of co-recursive polynomials of dimension d and some relations in the particular cases d = 3 and d = 4. Some properties of the dual sequence as well as of the corresponding Stieltjes functions are given.

scholarly journals Estimation of a Stieltjes function expanded to Taylor series at complex conjugate points

2009 ◽  
Vol 233 (3) ◽  
pp. 835-841 ◽  
Author(s):  
Stanisław Tokarzewski ◽  
Alphonse Ph. Magnus ◽  
Jacek Gilewicz
Keyword(s):  
Taylor Series ◽  
Conjugate Points ◽  
Complex Conjugate ◽  
Stieltjes Function

scholarly journals The Stieltjes function―definition and properties

1988 ◽  
Vol 51 (183) ◽  
pp. 281-281
Author(s):  
Jan Bohman ◽  
Carl-Erik Fr{öberg
Keyword(s):  
Stieltjes Function ◽  
Function Definition

Toda chain, Stieltjes function, and orthogonal polynomials

2007 ◽  
Vol 151 (1) ◽  
pp. 505-528 ◽  
Author(s):  
F. Peherstorfer ◽  
V. P. Spiridonov ◽  
A. S. Zhedanov
Keyword(s):  
Orthogonal Polynomials ◽  
Toda Chain ◽  
Stieltjes Function

scholarly journals Logarithmically complete monotonicity of a power-exponential function involving the logarithmic and psi functions

2015 ◽  
Vol 3 (2) ◽  
pp. 77
Author(s):  
Bai-Ni Guo ◽  
Feng Qi
Keyword(s):  
Exponential Function ◽  
Gamma Function ◽  
Unit Interval ◽  
Complete Monotonicity ◽  
Psi Function ◽  
Completely Monotonic Function ◽  
Stieltjes Function ◽  
Completely Monotonic ◽  
Logarithmically Completely Monotonic Function ◽  
Appl Math

Let \(\Gamma\) and \(\psi=\frac{\Gamma'}{\Gamma}\) be respectively the classical Euler gamma function and the psi function and let \(\gamma=-\psi(1)=0.57721566\dotsc\) stand for the Euler-Mascheroni constant. In the paper, the authors simply confirm the logarithmically complete monotonicity of the power-exponential function \(q(t)=t^{t[\psi(t)-\ln t]-\gamma}\) on the unit interval \((0,1)\), concisely deny that \(q(t)\) is a Stieltjes function, surely point out fatal errors appeared in the paper [V. Krasniqi and A. Sh. Shabani, On a conjecture of a logarithmically completely monotonic function, Aust. J. Math. Anal. Appl. 11 (2014), no.1, Art.5, 5 pages; Available online at http://ajmaa.org/cgi-bin/paper.pl?string=v11n1/V11I1P5.tex], and partially solve a conjecture posed in the article [B.-N. Guo, Y.-J. Zhang, and F. Qi, Refinements and sharpenings of some double inequalities for bounding the gamma function, J. Inequal. Pure Appl. Math. 9 (2008), no.1, Art.17; Available online at http://www.emis.de/journals/JIPAM/article953.html].

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