| 1. |
|
|
| 2. |
- Abdeljawad, Ahmed, et al.
(författare)
-
Characterizations of a class of Pilipovic spaces by powers of harmonic oscillator
- 2020
-
Ingår i: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. - : Springer. - 1578-7303 .- 1579-1505. ; 114:3, s. 1-13
-
Tidskriftsartikel (refereegranskat)abstract
- We show that a smooth function f on Rd belongs to the Pilipovic space Hbσ (Rd ) or the Pilipovic space H0,bσ (Rd ), if and only if the Lp norm of HN d f for N ≥ 0, satisfy certain types of estimates. Here Hd = |x|2 − Δx is the harmonic oscillator.
|
|
| 3. |
- Abdeljawad, Ahmed, et al.
(författare)
-
Liftings for ultra-modulation spaces, and one-parameter groups of Gevrey-type pseudo-differential operators
- 2020
-
Ingår i: Analysis and Applications. - : World Scientific. - 0219-5305 .- 1793-6861. ; 18:4, s. 523-583
-
Tidskriftsartikel (refereegranskat)abstract
- We deduce one-parameter group properties for pseudo-differential operators Op(a), where a belongs to the class Λ∗(ω0) of certain Gevrey symbols. We use this to show that there are pseudo-differential operators Op(a) and Op(b) which are inverses to each other, where a ∈ Λ∗(ω0) and b ∈ Λ∗(1/ω0). We apply these results to deduce lifting property for modulation spaces and construct explicit isomorphisms between them. For each weight functions ω,ω0 moderated by GRS submultiplicative weights, we prove that the Toeplitz operator (or localization operator) Tp(ω0) is an isomorphism from Mp,q(ω) to M(ω/ω0)p,q for every p,q ∈(0,∞]. © 2019 World Scientific Publishing Company.
|
|
| 4. |
- Abdeljawad, Ahmed, et al.
(författare)
-
Pseudo-Differential Calculus in Anisotropic Gelfand-Shilov Setting
- 2019
-
Ingår i: Integral equations and operator theory. - : Springer. - 0378-620X .- 1420-8989. ; 91:3
-
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.
|
|
| 5. |
- Cappiello, Marco, et al.
(författare)
-
Pseudo-differential operators in a Gelfand–Shilov setting
- 2017
-
Ingår i: Mathematische Nachrichten. - : John Wiley & Sons. - 0025-584X .- 1522-2616. ; 290:5-6, s. 738-755
-
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.
|
|
| 6. |
- Cappiello, Marco, et al.
(författare)
-
Radial symmetric elements and the Bargmann transform
- 2014
-
Ingår i: Integral transforms and special functions. - : Taylor & Francis. - 1065-2469 .- 1476-8291. ; 25:9, s. 756-764
-
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.
|
|
| 7. |
- Chen, Yuanyuan, et al.
(författare)
-
Factorizations and singular value estimates of operators with Gelfand-Shilov and Pilipovic' kernels
- 2018
-
Ingår i: Journal of Fourier Analysis and Applications. - : Springer. - 1069-5869 .- 1531-5851. ; 24:3, s. 666-698
-
Tidskriftsartikel (refereegranskat)abstract
- We prove that any linear operator with kernel in a Pilipovi{\'c} or Gelfand-Shilov spacecan be factorized by two operators in the same class. We also give links onnumerical approximations for such compositions. We apply these composition rulesto deduce estimates of singular values and establish Schatten-von Neumann propertiesfor such operators.
|
|
| 8. |
- Chen, Yuanyuan, et al.
(författare)
-
Hilbert space embeddings for Gelfand–Shilov and Pilipović spaces
- 2017
-
Ingår i: Generalized Functions and Fourier Analysis. - Cham : Springer. - 9783319519104 - 9783319519111 ; , s. 31-44
-
Bokkapitel (refereegranskat)abstract
- We consider quasi-Banach spaces that lie between a Gelfand–Shilov space, or more generally, Pilipovi´c space, H, and its dual, H′. We prove that for such quasi-Banach space B, there are convenient Hilbert spaces, Hk, k=1,2ss, with normalized Hermite functions as orthonormal bases and such that B lies between H1 and H1, and the latter spaces lie between H and H′.
|
|
| 9. |
- Chen, Yuanyuan, et al.
(författare)
-
The Weyl product on quasi-Banach modulation spaces
- 2019
-
Ingår i: Bulletin of Mathematical Sciences. - : World Scientific. - 1664-3607 .- 1664-3615. ; 9:2, s. 1-30
-
Tidskriftsartikel (refereegranskat)abstract
- We study the bilinear Weyl product acting on quasi-Banach modulation spaces. We find sufficient conditions for continuity of the Weyl product and we derive necessary conditions. The results extend known results for Banach modulation spaces.
|
|
| 10. |
- Cordero, Elena, et al.
(författare)
-
Sharp results for the Weyl product on modulation spaces
- 2014
-
Ingår i: Journal of Functional Analysis. - : Elsevier. - 0022-1236 .- 1096-0783. ; 267:8, s. 3016-3057
-
Tidskriftsartikel (refereegranskat)abstract
- We give sufficient and necessary conditions on the Lebesgue exponentsfor the Weyl product to be bounded on modulation spaces. The sufficient conditions are obtained as the restriction to N=2 of aresult valid for the N-fold Weyl product. As a byproduct, we obtain sharpconditions for the twisted convolution to be bounded on Wieneramalgam spaces.
|
|
