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A note on the heat kernel on the Heisenberg group

Published online by Cambridge University Press:  17 April 2009

Adam Sikora  and
Jacek Zienkiewicz
Adam Sikora
Affiliation:
Department of Mathematical Sciences, New Mexico State University, PO Box 30001, Las Cruces NM 88003, Untied States of America e-mail: [email protected]
Jacek Zienkiewicz
Affiliation:
Instytut Matematyczuy, Uniwersytet Wroclawski, 50–384 Wroclaw, pl. Grunwaldzki 2/4, Poland e-mail: [email protected]
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Abstract

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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 operater 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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 1 , February 2002 , pp. 115 - 120
Copyright
Copyright © Australian Mathematical Society 2002

References

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