Characterizations of nuclear pseudo-differential operators on $${\mathbb {S}}^1$$ S 1 with applications to adjoints and products

Ghaemi, Mohammad Bagher; Birgani, Majid Jamalpour; Wong, M. W.

doi:10.1007/s11868-017-0199-7

Cited by 17 publications

(14 citation statements)

References 17 publications

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“…We prove Theorem 3.1 regarding the characterization of s-nuclear multilinear operators on abstract σ-finite measure spaces, and Theorem 3.2 and Theorem 3.3 regarding the characterization of s-nuclearity of periodic and discrete pseudo-differential operators. Although these theorems are multilinear extensions of the results due to Delgado [16], Delgado and Wong [17], JamalpourBirgani [26] and Ghaemi, JamalpourBirgani and Wong [20], we can recover their results from our results by considering r = 1. In order to study these multilinear operators admitting s-nuclear extensions, we prove the following multilinear version of a result by Delgado, on the nuclearity of integral operators on Lebesgue spaces (see [16], [18]).…”

Section: Boundedness Of Pseudo-differential Operators On T N and Z Nsupporting

confidence: 79%

Multilinear analysis for discrete and periodic pseudo-differential operators inLp-spaces

Cardona¹,

Kumar²

2018

revint

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In this note we announce our investigation on the L p properties for periodic and discrete multilinear pseudo-differential operators. First, we review the periodic analysis of multilinear pseudo-differential operators by showing classical multilinear Fourier multipliers theorems (proved by Coifman and Meyer, Tomita, Miyachi, Fujita, Grafakos, Tao, etc.) in the context of periodic and discrete multilinear pseudo-differential operators. For this, we use the periodic analysis of pseudo-differential operators developed by Ruzhansky and Turunen. The s-nuclearity, 0 < s ≤ 1, for the discrete and periodic multilinear pseudo-differential operators will be investigated. To do so, we classify those s-nuclear, 0 < s ≤ 1, multilinear integral operators on arbitrary Lebesgue spaces defined on σ-finite measures spaces. Finally, we present some applications of our analysis to deduce the periodic Kato-Ponce inequality and to examine the s-nuclearity of multilinear Bessel potentials as well as the s-nuclearity of periodic Fourier integral operators admitting suitable types of singularities.

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Section: Boundedness Of Pseudo-differential Operators On T N and Z Nsupporting

confidence: 79%

Multilinear analysis for discrete and periodic pseudo-differential operators inLp-spaces

Cardona¹,

Kumar²

2018

revint

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“…The previous results are analogues of the main results proved in Ghaemi, Jamalpour Birgani, and Wong [29], [30], Jamalpour Birgani [36], and Cardona and Barraza [3]. Theorem 1.1, can be used for understanding the properties of the corresponding symbols in Lebesgue spaces.…”

Section: Nuclear Fourier Integral Operatorssupporting

confidence: 59%

“…The last condition have been proved for pseudo-differential operators in [29]. In this case, the nuclear trace of F can be written as…”

Section: Fios On Compact Lie Groupsmentioning

confidence: 96%

“…On the other hand, characterizations for nuclear operators in terms of decomposition of the symbol trough of the Fourier transform were investigated by Ghaemi, Jamalpour Birgani, and Wong in [29], [30], [36] for S 1 , Z, and also for arbitrary compact and Hausdorff groups. Finally the subject has been considered for pseudo-multipliers associated to the harmonic oscillator (which can be qualified as pseudo-differential operators according to the Ruzhansky-Tokmagambetov calculus when the reference operators is the quantum harmonic oscillator) in the works of the author [3], [7], [8].…”

Section: Outline Of the Papermentioning

confidence: 99%

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On the nuclear trace of Fourier integral operators

Cardona

2019

revint

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In this paper we characterise ther-nuclearity of Fourier integraloperators on Lebesgue spaces. Fourier integral operators will be consideredinRn,the discrete groupZn,then-dimensional torus and symmetric spaces(compact homogeneous manifolds). We also give formulae forthe nucleartrace of these operators. Explicit examples will be given onZn,the torusTn,the special unitary group SU(2),and the projective complex planeCP2.Ourmain theorems will be applied to the characterization ofr-nuclear pseudo-differential operators defined by the Weyl quantization procedure.

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“…The nuclearity of pseudo-differential operators on R n has been studied by Aoki [2] and Rempala [36]. Characterizations of nuclear operators in terms of decomposition of symbol through Fourier transform were investigated by Ghaemi, Jamalpour Birgani and Wong for S 1 [19]. Later they generalized their results on nuclearity to the pseudo-differential operators for any arbitrary compact group [20].…”

Section: Introductionmentioning

confidence: 99%

Nuclearity of operators related to finite measure spaces

Kumar

Mondal

2020

J. Pseudo-Differ. Oper. Appl.

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Let (S, B, m) be a finite measure space. The aim of this paper is to give necessary and sufficient conditions on symbols such that the corresponding Z-operator from L p 1 (Z) into L p 2 (Z) and S-operator from L p 1 (S) into L p 2 (S) to be nuclear for 1 ≤ p 1 , p 2 < ∞. We show that the adjoint of the nuclear Z-operator from L p 2 into L p 1 is again a nuclear operator. As applications, we get the symbol of the product of the nuclear operators with bounded operators.

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Characterizations of nuclear pseudo-differential operators on $${\mathbb {S}}^1$$ S 1 with applications to adjoints and products

Cited by 17 publications

References 17 publications

Multilinear analysis for discrete and periodic pseudo-differential operators inLp-spaces

Multilinear analysis for discrete and periodic pseudo-differential operators inLp-spaces

On the nuclear trace of Fourier integral operators

Nuclearity of operators related to finite measure spaces

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