Metamorphism—an integral transform reducing the order of a differential equation

References

[1] S. T. Ali, J.-P. Antoine and J.-P. Gazeau, Coherent States, Wavelets, and their Generalizations, 2nd ed., Theoret. Math. Phys., Springer, New York, 2014. 10.1007/978-1-4614-8535-3Search in Google Scholar

[2] F. Almalki and V. V. Kisil, Geometric dynamics of a harmonic oscillator, arbitrary minimal uncertainty states and the smallest step 3 nilpotent Lie group, J. Phys. A 52 (2019), no. 2, Article ID 025301. 10.1088/1751-8121/aaed4dSearch in Google Scholar

[3] F. Almalki and V. V. Kisil, Solving the Schrödinger equation by reduction to a first-order differential operator through a coherent states transform, Phys. Lett. A 384 (2020), no. 16, Article ID 126330. 10.1016/j.physleta.2020.126330Search in Google Scholar

[4] T. Alqurashi and V. V. Kisil, Metamorphism as a covariant transform for the SSR group, preprint (2023), https://arxiv.org/abs/2301.05879. 10.1007/s40590-023-00505-3Search in Google Scholar

[5] 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

[6] R. Berndt, Representations of Linear Groups: An Introduction Based on Examples from Physics and Number Theory, Vieweg, Wiesbaden, 2007. Search in Google Scholar

[7] M. J. Colbrook and A. V. Kisil, A Mathieu function boundary spectral method for scattering by multiple variable poro-elastic plates, with applications to metamaterials and acoustics, Proc. A. 476 (2020), no. 2241, Article ID 20200184. 10.1098/rspa.2020.0184Search in Google Scholar PubMed PubMed Central

[8] A. Córdoba and C. Fefferman, Wave packets and Fourier integral operators, Comm. Partial Differential Equations 3 (1978), no. 11, 979–1005. 10.1080/03605307808820083Search in Google Scholar

[9] G. B. Folland, Harmonic Analysis in Phase Space, Ann. of Math. Stud. 122, Princeton University, Princeton, 1989. 10.1515/9781400882427Search in Google Scholar

[10] V. V. Kisil, Symbolic calculation for covariant transform on the SSR group, Technical report, 2021, https://github.com/vvkisil/SSR-group-computations. Search in Google Scholar

[11] V. V. Kravchenko and S. M. Sitnik, Some recent developments in the transmutation operator approach, Transmutation Operators and Applications, Trends Math., Birkhäuser/Springer, Cham (2020), 3–9. 10.1007/978-3-030-35914-0_1Search in Google Scholar

[12] W. Miller, Jr., Lie Theory and Special Functions, Math. Sci. Eng. 43, Academic Press, New York, 1968. Search in Google Scholar

[13] W. Miller, Jr., Symmetry and Separation of Variables, Encyclopedia Math. Appl. 4, Addison-Wesley, Reading, 1977. Search in Google Scholar

[14] Y. A. Neretin, Lectures on Gaussian Integral Operators and Classical Groups, EMS Ser. Lect. Math., European Mathematical Society, Zürich, 2011. 10.4171/080Search in Google Scholar

[15] V. F. Osipov, Almost-Periodic Functions of Bohr–Fresnel (in Russian), Gosudarstvennyĭ Universitet, St. Petersburg, 1992. Search in Google Scholar

[16] S.-C. Pei and J.-J. Ding, Eigenfunctions of the linear canonical transform, Linear Canonical Transforms, Springer Ser. Optical Sci. 198, Springer, New York (2016), 81–96. 10.1007/978-1-4939-3028-9_3Search in Google Scholar

[17] A. D. Polyanin and V. E. Nazaikinskii, Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd ed., CRC Press, Boca Raton, 2016. 10.1201/b19056Search in Google Scholar

[18] A. D. Polyanin, V. F. Zaitsev and A. Moussiaux, Handbook of First Order Partial Differential Equations, Diff. Integral Equations Appl. 1, Taylor & Francis, London, 2002. 10.1201/b16828Search in Google Scholar

[19] I. E. Segal, Mathematical Problems of Relativistic Physics, Lectures Appl. Math. 1960, American Mathematical Society, Providence, 1963. Search in Google Scholar

[20] N. J. Vilenkin, Special Functions and the Theory of group Representations, Transl. Math. Monogr. 22, American Mathematical Society, Providence, 1968. 10.1090/mmono/022Search in Google Scholar

[21] A. H. Zemanian, A generalized Weierstrass transformation, SIAM J. Appl. Math. 15 (1967), 1088–1105. 10.1137/0115093Search in Google Scholar