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Explicit fundamental solution for the operator $$L+\alpha |T|$$ on the Gelfand pair $$(\mathbb {H}_{n},U(n))$$. by I. E. Cardoso; M. Subils; R. E. Vidal is a Mathematics article available to read on EtoBox.
What is Explicit fundamental solution for the operator $$L+\alpha |T|$$ on the Gelfand pair $$(\mathbb {H}_{n},U(n))$$. about?
By means of the spherical functions associated to the Gelfand pair (H n , U (n)) we define the operator L + α|T |, where L denotes the Heisenberg sublaplacian and T denotes the central element of the Heisenberg Lie algebra, we establish a notion of fundamental solution and explicitly compute in terms of the Gauss hypergeometric function. For α < n we use the Integral Representation Theorem to obtain a more detailed expression. Finally, we remark that when α = 0 we recover the fundamental solution for the Heisenberg sublaplacian given by Folland. ## Keywords Heisenberg group • Fundamental solution of pseudodifferential operator • Gelfand pair • Spherical functions Mathematics Subject Classification 47G30 • 58J40 u • (z, t) = (u(z), t).
Who reads Explicit fundamental solution for the operator $$L+\alpha |T|$$ on the Gelfand pair $$(\mathbb {H}_{n},U(n))$$.?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- I. E. Cardoso; M. Subils; R. E. Vidal
- Publisher
- Springer Science and Business Media LLC
- Published
- 2021
- Language
- EN
- Field
- Mathematics (Physical Sciences)