A note on the heat kernel on the Heisenberg group

Adam Sikora; Jacek Zienkiewicz

doi:10.1017/s0004972700020128

A note on the heat kernel on the Heisenberg group

Adam Sikora, Jacek Zienkiewicz

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We describe the analytic continuation of the heat kernel on the Heisenberg group ℍ_n(ℝ). As a consequence, we show that the convolution kernel corresponding to the Schrödinger operator e^isL is a smooth function on ℍ_n(ℝ) \ S_s, where S_s = ((0,0,±sk) ∈ ℍ_n(ℝ): k = n, n + 2, n + 4, …). At every point of S_s the convolution kernel of e^isL has a singularity of Calderón-Zygmund type.

Original language	English
Pages (from-to)	115-120
Number of pages	6
Journal	Bulletin of the Australian Mathematical Society
Volume	65
Issue number	1
DOIs	https://doi.org/10.1017/s0004972700020128
Publication status	Published - 2002
Externally published	Yes

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title = "A note on the heat kernel on the Heisenberg group",

abstract = "We describe the analytic continuation of the heat kernel on the Heisenberg group ℍn(ℝ). As a consequence, we show that the convolution kernel corresponding to the Schr{\"o}dinger operator eisL is a smooth function on ℍn(ℝ) \ Ss, where Ss = ((0,0,±sk) ∈ ℍn(ℝ): k = n, n + 2, n + 4, …). At every point of Ss the convolution kernel of eisL has a singularity of Calder{\'o}n-Zygmund type.",

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AB - We describe the analytic continuation of the heat kernel on the Heisenberg group ℍn(ℝ). As a consequence, we show that the convolution kernel corresponding to the Schrödinger operator eisL is a smooth function on ℍn(ℝ) \ Ss, where Ss = ((0,0,±sk) ∈ ℍn(ℝ): k = n, n + 2, n + 4, …). At every point of Ss the convolution kernel of eisL has a singularity of Calderón-Zygmund type.

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JO - Bulletin of the Australian Mathematical Society

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A note on the heat kernel on the Heisenberg group

Abstract

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