Abstract
In this paper, we give some applications of the Dunkl-type Segal–Bargmann transform
Acknowledgements
The authors would like to thank the referee for the careful reading and editing of the paper.
References
[1] A. Aftalion, X. Blanc and F. Nier, Lowest Landau level functional and Bargmann spaces for Bose–Einstein condensates, J. Funct. Anal. 241 (2006), no. 2, 661–702. 10.1016/j.jfa.2006.04.027Search in Google Scholar
[2] B. Amri and A. Hammi, Dunkl–Schrödinger operators, Complex Anal. Oper. Theory 13 (2019), no. 3, 1033–1058. 10.1007/s11785-018-0834-1Search in Google Scholar
[3] B. Amri and A. Hammi, Semigroup and Riesz transform for the Dunkl–Schrödinger operators, Semigroup Forum 101 (2020), no. 3, 507–533. 10.1007/s00233-020-10106-5Search in Google Scholar
[4] V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform, Comm. Pure Appl. Math. 14 (1961), 187–214. 10.1002/cpa.3160140303Search in Google Scholar
[5] V. Bargmann, On a Hilbert space of analytic functions and an associated integral transform. Part II. A family of related function spaces. Application to distribution theory, Comm. Pure Appl. Math. 20 (1967), 1–101. 10.1002/cpa.3160200102Search in Google Scholar
[6] S. Ben Saïd and B. Ørsted, Segal–Bargmann transforms associated with finite Coxeter groups, Math. Ann. 334 (2006), no. 2, 281–323. 10.1007/s00208-005-0718-3Search in Google Scholar
[7] C. A. Berger and L. A. Coburn, Toeplitz operators on the Segal–Bargmann space, Trans. Amer. Math. Soc. 301 (1987), no. 2, 813–829. 10.1090/S0002-9947-1987-0882716-4Search in Google Scholar
[8] N. Berline, E. Getzler and M. Vergne, Heat Kernels and Dirac Operators, Grundlehren Text Editions, Springer, Berlin, 2004. Search in Google Scholar
[9] Y. Chen and K. Zhu, Uncertainty principles for the Fock space, Sci. Sinica Math. 45 (2015), no. 11, 1847–1854. 10.1360/N012015-00057Search in Google Scholar
[10] F. M. Cholewinski, Generalized Fock spaces and associated operators, SIAM J. Math. Anal. 15 (1984), no. 1, 177–202. 10.1137/0515015Search in Google Scholar
[11] B. K. Driver and B. C. Hall, Yang–Mills theory and the Segal–Bargmann transform, Comm. Math. Phys. 201 (1999), no. 2, 249–290. 10.1007/s002200050555Search in Google Scholar
[12] C. F. Dunkl, Differential-difference operators associated to reflection groups, Trans. Amer. Math. Soc. 311 (1989), no. 1, 167–183. 10.1090/S0002-9947-1989-0951883-8Search in Google Scholar
[13] C. F. Dunkl, Integral kernels with reflection group invariance, Canad. J. Math. 43 (1991), no. 6, 1213–1227. 10.4153/CJM-1991-069-8Search in Google Scholar
[14] A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcendental Functions. Vols. I, II, McGraw-Hill, New York, 1953. Search in Google Scholar
[15] L. C. Evans, Partial Differential Equations, Grad. Stud. Math. 19, American Mathematical Society, Providence, 1998. Search in Google Scholar
[16]
A. Fitouhi,
Heat “polynomials” for a singular differential operator on
[17] L. Lapointe and L. Vinet, Exact operator solution of the Calogero–Sutherland model, Comm. Math. Phys. 178 (1996), no. 2, 425–452. 10.1007/BF02099456Search in Google Scholar
[18] Y. Le Floch, Bounds for fidelity of semiclassical Lagrangian states in Kähler quantization, J. Math. Phys. 59 (2018), no. 8, Article ID 082103. 10.1063/1.5030410Search in Google Scholar
[19] A. Y. O. Mohameden and M. V. O. Moustapha, Wave kernels for the Dirac, Euler operators and the harmonic oscillator, J. Math. Phys. 55 (2014), no. 3, Article ID 031503. 10.1063/1.4867620Search in Google Scholar
[20] M. Rosenblum, Generalized Hermite polynomials and the Bose-like oscillator calculus, Nonselfadjoint Operators and Related Topics (Beer Sheva 1992), Oper. Theory Adv. Appl. 73, Birkhäuser, Basel (1994), 369–396. 10.1007/978-3-0348-8522-5_15Search in Google Scholar
[21] M. Rösler, Generalized Hermite polynomials and the heat equation for Dunkl operators, Comm. Math. Phys. 192 (1998), no. 3, 519–542. 10.1007/s002200050307Search in Google Scholar
[22] O. Rouby, J. Sjöstrand and S. V. Ngọc, Analytic Bergman operators in the semiclassical limit, Duke Math. J. 169 (2020), no. 16, 3033–3097. 10.1215/00127094-2020-0022Search in Google Scholar
[23] A. Saidi, A. Y. Mahmoud and M. V. O. Moustapha, Bargmann transform with application to time-dependent Schrödinger equation, Int. J. Sci. Tech. Res. 9 (2020), no. 2, 760–763. Search in Google Scholar
[24] M. Sifi and F. Soltani, Generalized Fock spaces and Weyl relations for the Dunkl kernel on the real line, J. Math. Anal. Appl. 270 (2002), no. 1, 92–106. 10.1016/S0022-247X(02)00052-5Search in Google Scholar
[25] F. Soltani, Generalized Fock spaces and Weyl commutation relations for the Dunkl kernel, Pacific J. Math. 214 (2004), no. 2, 379–397. 10.2140/pjm.2004.214.379Search in Google Scholar
[26]
F. Soltani,
Inversion formulas in the Dunkl-type heat conduction on
[27] F. Soltani, Inversion formulas for the Dunkl-type Segal–Bargmann transform, Integral Transforms Spec. Funct. 26 (2015), no. 5, 325–339. 10.1080/10652469.2015.1004331Search in Google Scholar
[28] F. Soltani, Uncertainty principles for the Dunkl-type Segal–Bargmann transform, Complex Anal. Oper. Theory 11 (2017), no. 3, 475–490. 10.1007/s11785-016-0588-6Search in Google Scholar
[29] F. Soltani, Uncertainty principles for the Segal–Bargmann transform, J. Math. Res. Appl. 37 (2017), no. 5, 563–576. Search in Google Scholar
[30] F. Soltani and A. Nemri, Analytical and numerical approximation formulas on the Dunkl-type Fock spaces, Acta Math. Vietnam. 42 (2017), no. 1, 129–147. 10.1007/s40306-016-0188-6Search in Google Scholar
[31]
F. Soltani and M. Nenni,
Difference and primitive operators on the Dunkl-type Fock space
[32] F. Soltani and M. Nenni, Heisenberg uncertainty principles for the Dunkl-type Fock space, Complex Anal. Oper. Theory 17 (2023), no. 6, Paper No. 105. 10.1007/s11785-023-01408-xSearch in Google Scholar
[33] K. Zhu, Analysis on Fock Spaces, Grad. Texts in Math. 263, Springer, New York, 2012. 10.1007/978-1-4419-8801-0Search in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- A note on higher order Dirac operators in Clifford analysis
- Action of higher derivations on semiprime rings
- Demicompact linear operator. Essential pseudospectra and perturbation
- On the rotations and limit cycles of solutions to the basic system of equations
- On the criteria of a measure of non-strict cosingularity in the description of spectral properties of operator matrix
- A class of nontrivial simple examples of a non-D-space
- A study on Fibo-Pascal sequence spaces and associated matrix transformations and applications of Hausdorff measure of non-compactness
- A property of the free Gaussian distribution
- The influence of c-subnormality subgroups on the structure of finite groups
- Wave propagation on hexagonal lattices
- Timelike zero mean curvature surfaces in ℝ1 4
- A Mazurkiewicz set containing the graph of a Sierpiński–Zygmund function
- On corrected Simpson-type inequalities via local fractional integrals
- Sobolev regularity for a class of local fractional new maximal operators
- On the singular directions of a holomorphic mapping in P n(ℂ)
- On minimal surfaces in ℍ2 × ℝ space
- Ulyanov inequalities for the mixed moduli of smoothness in mixed metrics
- Dunkl-type Segal–Bargmann transform and its applications to some partial differential equations
- On generalized derivations in factor rings
- Remarks on generalized derivations in factor rings
Articles in the same Issue
- Frontmatter
- A note on higher order Dirac operators in Clifford analysis
- Action of higher derivations on semiprime rings
- Demicompact linear operator. Essential pseudospectra and perturbation
- On the rotations and limit cycles of solutions to the basic system of equations
- On the criteria of a measure of non-strict cosingularity in the description of spectral properties of operator matrix
- A class of nontrivial simple examples of a non-D-space
- A study on Fibo-Pascal sequence spaces and associated matrix transformations and applications of Hausdorff measure of non-compactness
- A property of the free Gaussian distribution
- The influence of c-subnormality subgroups on the structure of finite groups
- Wave propagation on hexagonal lattices
- Timelike zero mean curvature surfaces in ℝ1 4
- A Mazurkiewicz set containing the graph of a Sierpiński–Zygmund function
- On corrected Simpson-type inequalities via local fractional integrals
- Sobolev regularity for a class of local fractional new maximal operators
- On the singular directions of a holomorphic mapping in P n(ℂ)
- On minimal surfaces in ℍ2 × ℝ space
- Ulyanov inequalities for the mixed moduli of smoothness in mixed metrics
- Dunkl-type Segal–Bargmann transform and its applications to some partial differential equations
- On generalized derivations in factor rings
- Remarks on generalized derivations in factor rings