New characterizations of completely monotone functions and Bernstein functions, a converse to Hausdorff’s moment characterization theorem

Aguech, Rafik; Jedidi, Wissem

doi:10.1016/j.ajmsc.2018.03.001

Cited by 8 publications

(10 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…and the facts that BF is a closed convex cone, a simple proof for the characterization of L 0 (R + ) could be provided. For instance, see Aguech and Jedidi [1] for the following result.…”

Section: Simple Characterization Of Multiple Selfdecomposable Distrib...mentioning

confidence: 94%

See 1 more Smart Citation

Some characterizations of multiple selfdecomposability with extensions and an application to the Gamma function

Jedidi¹,

Jurek²,

Al³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Inspirations for this paper can be traced to Urbanik [48] where convolution semigroups of multiple decomposable distributions were introduced. In particular, the classical gamma G t and log G t , t > 0 variables are selfdecomposable. In fact, we show that log G t is twice selfdecomposable if, and only if, t ≥ t 1 ≈ 0.15165. Moreover, we provide several new factorizations of the Gamma function and the Gamma distributions. To this end, we revisit the class of multiply selfdecomposable distributions, denoted L n (R), and propose handy tools for its characterization, mainly based on the Mellin-Euler's differential operator. Furthermore, we also give a perspective of generalization of the class L n (R) based on linear operators or on stochastic integral representations.

show abstract

“…and the facts that BF is a closed convex cone, a simple proof for the characterization of L 0 (R + ) could be provided. For instance, see Aguech and Jedidi [1] for the following result.…”

Section: Simple Characterization Of Multiple Selfdecomposable Distrib...mentioning

confidence: 94%

“….+ X n,n . Conversely, any infinitely divisible distribution can be obtained in the scheme (1); see Gnedenko and Kolmogorov [11] or Loève [30] or Parthasarathy [35], for multi-dimensional spaces.…”

Section: Introductionmentioning

confidence: 99%

Some characterizations of multiple selfdecomposability with extensions and an application to the Gamma function

Jedidi¹,

Jurek²,

Al³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…, p, regardless of the value of Z, the hypergeometric function is a polynomial of finite order, defined by the usual hypergeometric series that get cut at N = min(|a k | / a k ∈ −N 0 ), i.e., the minimal value between the modules of the a k 's that are negative integers, Next, we will limit only to the odd d case. 12 11 In fact, it can be seen from [19], that from the properties of completely monotonic functions, it is sufficient to impose the equality of l.h.s. and r.h.s.…”

Section: A Conformal Block Asymptotic Expansionmentioning

confidence: 99%

Interplay between reflection positivity and crossing symmetry in the bootstrap approach to CFT

Lanosa

Leston

Mario

2022

J. High Energ. Phys.

View full text Add to dashboard Cite

Crossing symmetry (CS) is the main tool in the bootstrap program applied to CFT. This consists in an equality which imposes restrictions on the CFT data of a model, i.e., the OPE coefficients and the conformal dimensions. Reflection positivity (RP) has also played a role in this program, since this condition is what leads to the unitary bound and reality of the OPE coefficients. In this paper, we show that RP can still reveal more information, explaining how RP itself can capture an important part of the restrictions imposed by the full CS equality. In order to do that, we use a connection used by us in a previous work between RP and positive definiteness of a function of a single variable. This allows us to write constraints on the OPE coefficients in a concise way. These constraints are encoded in the conditions that certain functions of the cross-ratio will be positive defined and in particular completely monotonic. We will consider how the bounding of scalar conformal dimensions and OPE coefficients arise in this RP based approach. We will illustrate the conceptual and practical value of this view trough examples of general CFT models in d-dimensions.

show abstract

“…. , p: 10 In fact, it can be seen from [18], that from the properties of completely monotonic functions, it is sufficient to impose the equality of lhs and rhs of the CS equation only at ρc integers from an arbitrary number N to +∞, for the equality to be satisfied at all ρ real numbers (or at all x reals in (0, 1))…”

Section: A Conformal Block Asymptotic Expansionmentioning

confidence: 99%

Interplay between reflection positivity and crossing symmetry in the bootstrap approach to CFT

Lanosa,

Leston,

Passaglia

2021

Preprint

View full text Add to dashboard Cite

Crossing symmetry (CS) is the main tool in the bootstrap program applied to CFT. This consists in an equality which imposes restrictions on the CFT data of a model, i.e., the OPE coefficients and the conformal dimensions. Reflection positivity (RP) has also played a role in this program, since this condition is what leads to the unitary bound and reality of the OPE coefficients. In this paper, we show that RP can still reveal more information, explaining how RP itself can capture an important part of the restrictions imposed by the full CS equality. In order to do that, we use a connection used by us in a previous work between RP and positive definiteness of a function of a single variable. This allows us to write constraints on the OPE coefficients in a concise way . These constraints are encoded in the conditions that certain functions of the cross-ratio will be positive defined and in particular completely monotonic. We will consider how the bounding of scalar conformal dimensions and OPE coefficients arise in this RP based approach. We will illustrate the conceptual and practical value of this view trough examples of general CFT models in d-dimensions.

show abstract

New characterizations of completely monotone functions and Bernstein functions, a converse to Hausdorff’s moment characterization theorem

Cited by 8 publications

References 8 publications

Some characterizations of multiple selfdecomposability with extensions and an application to the Gamma function

Some characterizations of multiple selfdecomposability with extensions and an application to the Gamma function

Interplay between reflection positivity and crossing symmetry in the bootstrap approach to CFT

Interplay between reflection positivity and crossing symmetry in the bootstrap approach to CFT

Contact Info

Product

Resources

About