| 1. |
- Abdeljawad, Ahmed, et al.
(författare)
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Pseudo-Differential Calculus in Anisotropic Gelfand-Shilov Setting
- 2019
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Ingår i: Integral equations and operator theory. - : Springer. - 0378-620X .- 1420-8989. ; 91:3
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Tidskriftsartikel (refereegranskat)abstract
- We study some classes of pseudo-differential operators with symbols a admitting anisotropic exponential type growth at infinity. We deduce mapping properties for these operators on Gelfand-Shilov spaces. Moreover, we deduce algebraic and certain invariance properties of these classes.
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| 2. |
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| 3. |
- Cappiello, Marco, et al.
(författare)
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Conormal distributions in the Shubin calculus of pseudodifferential operators
- 2018
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Ingår i: Journal of Mathematical Physics. - : American Institute of Physics (AIP). - 0022-2488 .- 1089-7658. ; 59:2
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Tidskriftsartikel (refereegranskat)abstract
- We characterize the Schwartz kernels of pseudodifferential operators of Shubin type by means of a Fourier-Bros-Iagolnitzer transform. Based on this, we introduce as a generalization a new class of tempered distributions called Shubin conormal distributions. We study their transformation behavior, normal forms, and microlocal properties.
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| 4. |
- Cappiello, Marco, et al.
(författare)
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Lagrangian Distributions and Fourier Integral Operators with Quadratic Phase Functions and Shubin Amplitudes
- 2020
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Ingår i: Publications of the Research Institute for Mathematical Sciences. - : European Mathematical Society Publishing House. - 0034-5318 .- 1663-4926. ; 56:3, s. 561-602
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Tidskriftsartikel (refereegranskat)abstract
- We study Fourier integral operators with Shubin amplitudes and quadratic phase functions associated to twisted graph Lagrangians with respect to symplectic matrices. We factorize such an operator as a pseudodifferential operator and a metaplectic operator. Extending the conormal distributions adapted to the Shubin calculus, we define an adapted notion of Lagrangian tempered distribution. We show that the kernels of Fourier integral operators are identical to Lagrangian distributions with respect to twisted graph Lagrangians.
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| 5. |
- Cappiello, Marco, et al.
(författare)
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On the Inverse to the Harmonic Oscillator
- 2015
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Ingår i: Communications in Partial Differential Equations. - : Informa UK Limited. - 0360-5302 .- 1532-4133. ; 40:6, s. 1096-1118
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Tidskriftsartikel (refereegranskat)abstract
- Let b ( d ) be the Weyl symbol of the inverse to the harmonic oscillator on R- d . We prove that b ( d ) and its derivatives satisfy convenient bounds of Gevrey and Gelfand-Shilov type, and obtain explicit expressions for b ( d ). In the even-dimensional case we characterize b ( d ) in terms of elementary functions. In the analysis we use properties of radial symmetry and a combination of different techniques involving classical a priori estimates, commutator identities, power series and asymptotic expansions.
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| 6. |
- Cappiello, Marco, et al.
(författare)
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Pseudo-differential operators in a Gelfand–Shilov setting
- 2017
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Ingår i: Mathematische Nachrichten. - : John Wiley & Sons. - 0025-584X .- 1522-2616. ; 290:5-6, s. 738-755
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Tidskriftsartikel (refereegranskat)abstract
- We introduce some general classes of pseudodifferential operators with symbols admitting exponential type growth at infinity and we prove mapping properties for these operators on Gelfand–Shilov spaces. Moreover, we deduce composition and certain invariance properties of these classes.
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| 7. |
- Cappiello, Marco, et al.
(författare)
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Radial symmetric elements and the Bargmann transform
- 2014
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Ingår i: Integral transforms and special functions. - : Taylor & Francis. - 1065-2469 .- 1476-8291. ; 25:9, s. 756-764
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Tidskriftsartikel (refereegranskat)abstract
- We prove that a function or distribution on R^d is radial symmetric, if and only if its Bargmann transform is a composition by an entire function on C and the canonical quadratic function from C^d to C.
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| 8. |
- Cappiello, Marco, et al.
(författare)
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Shubin type Fourier integral operators and evolution equations
- 2020
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Ingår i: Journal of Pseudo-Differential Operators and Applications. - : Springer. - 1662-9981 .- 1662-999X. ; 11:1, s. 119-139
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Tidskriftsartikel (refereegranskat)abstract
- We study the Cauchy problem for an evolution equation of Schrödinger type. The Hamiltonian is the Weyl quantization of a real homogeneous quadratic form with a pseudodifferential perturbation of negative order from Shubin’s class. We prove that the propagator is a Fourier integral operator of Shubin type of order zero. Using results for such operators and corresponding Lagrangian distributions, we study the propagator and the solution, and derive phase space estimates for them.
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