Abstract
If X and Y are two vector fields, or in general, two operators which commute, i.e., XY = YX, then it is obvious that their squares also commute. If \(\mathbb{L} = \frac{1} {2}({X}^{2} + {Y }^{2})\) with [X 2, Y 2] = 0, then the problem of finding the heat kernel for \(\mathbb{L}\) is reduced to the same problem for the operators X 2 and Y 2, with
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© 2011 Springer Science+Business Media, LLC
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Calin, O., Chang, DC., Furutani, K., Iwasaki, C. (2011). Commuting Operators. In: Heat Kernels for Elliptic and Sub-elliptic Operators. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4995-1_4
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DOI: https://doi.org/10.1007/978-0-8176-4995-1_4
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Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4994-4
Online ISBN: 978-0-8176-4995-1
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