Factorization of integral transformations of convolution type

Brychkov, Yu. A.; Glaeske, Hans‐Jürgen; Marichev, O. I.

doi:10.1007/bf02105396

Cited by 17 publications

(17 citation statements)

References 9 publications

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“…Then M j is a unitary operator from L 2 (U j ) to L 2 (R n ). This can be easily obtained from the Plancherel theorem for the n-dimensional Fourier transform by using an exponential change of variables (see [3]). Moreover, if we assume that |y| −1/2 f (y) ∈ L 1 (U) then making use of Fubini's theorem, and integrating by substitution x = A ′ (u) −1 y yield the following (s ∈ R n ):…”

Section: This Is a Bounded Hausdorff Operator Inmentioning

confidence: 99%

“…The map M is a bounded operator from L p (U) to L q (R n ) if 1 ≤ p ≤ 2 (1/p + 1/q = 1) and a unitary operator from L 2 (U) to L 2 (R n ). This can be easily obtained from the Hausdorff-Young inequality (and from the Plancherel theorem if p = 2) for the n-dimensional Fourier transform by using an exponential change of variables (see [3]). Let f ∈ L p (U).…”

Section: Examplementioning

confidence: 99%

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On the Structure of Normal Hausdorff Operators on Lebesgue Spaces

Миротин

2019

Funct Anal Its Appl

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Section: This Is a Bounded Hausdorff Operator Inmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

On the Structure of Normal Hausdorff Operators on Lebesgue Spaces

Миротин

2019

Funct Anal Its Appl

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show abstract

“…Then M i is a unitary operator acting from L 2 (U i ) to L 2 (R n ). This can be easily obtained from the Plancherel theorem for the Fourier transform by using an exponential change of variables (see [4]). Moreover, if we assume that |y| −1/2 f (y) ∈ L 1 (U j ) then making use of Fubini's theorem, and integrating by substitution x = A ′ (u) −1 y = (y 1 /a 1 (u); .…”

Section: Notation and Preliminariesmentioning

confidence: 99%

On the description of multidimensional normal Hausdorff operators on Lebesgue spaces

Миротин

2019

Forum Mathematicum

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AbstractHausdorff operators originated from some classical summation methods. Now this is an active research field. In the present article, a spectral representation for multidimensional normal Hausdorff operator is given. We show that normal Hausdorff operator in {L^{2}(\mathbb{R}^{n})} is unitary equivalent to the operator of multiplication by some matrix-valued function (its matrix symbol) in the space {L^{2}(\mathbb{R}^{n};\mathbb{C}^{2^{n}})}. Several corollaries that show that properties of a Hausdorff operator are closely related to the properties of its symbol are considered. In particular, the norm and the spectrum of such operators are described in terms of the symbol.

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“…From Assumption 3 and Theorem 2.1 in Brychkov et al (1992), it follows that the Laplace exponent biv …”

Section: Proof Identification Of the Regressor Functionsmentioning

confidence: 99%

Study of the bivariate survival data using frailty models based on Lévy processes

Begun

Yashin

2018

AStA Adv Stat Anal

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Frailty models allow us to take into account the non-observable inhomogeneity of individual hazard functions. Although models with time-independent frailty have been intensively studied over the last decades and a wide range of applications in survival analysis have been found, the studies based on the models with time-dependent frailty are relatively rare. In this paper, we formulate and prove two propositions related to the identifiability of the bivariate survival models with frailty given by a nonnegative bivariate Lévy process. We discuss parametric and semiparametric procedures for estimating unknown parameters and baseline hazard functions. Numerical experiments with simulated and real data illustrate these procedures. The statements of the propositions can be easily extended to the multivariate case.

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Factorization of integral transformations of convolution type

Cited by 17 publications

References 9 publications

On the Structure of Normal Hausdorff Operators on Lebesgue Spaces

On the Structure of Normal Hausdorff Operators on Lebesgue Spaces

On the description of multidimensional normal Hausdorff operators on Lebesgue spaces

Study of the bivariate survival data using frailty models based on Lévy processes

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