Sub-Laplacians with Drift on Lie Groups of Polynomial Volume Growth

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9780821827642: Sub-Laplacians with Drift on Lie Groups of Polynomial Volume Growth

We prove a parabolic Harnack inequality for a centered sub-Laplacian $L$ on a connected Lie group $G$ of polynomial volume growth by using ideas from Homogenisation theory and by adapting the method of Krylov and Safonov. We use this inequality to obtain a Taylor formula for the heat functions and thus we also obtain Harnack inequalities for their space and time derivatives. We characterise the harmonic functions which grow polynomially. We obtain Gaussian estimates for the heat kernel and estimates similar to the classical Berry-Esseen estimate. Finally, we study the associated Riesz transform operators. If $L$ is not centered, then we can conjugate $L$ by a convenient multiplicative function and obtain another centered sub-Laplacian $L_C$. Thus our results also extend to non-centered sub-Laplacians.

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Georgios K. Alexopoulos
Published by American Mathematical Society (2002)
ISBN 10: 0821827642 ISBN 13: 9780821827642
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Book Description American Mathematical Society, 2002. Mass Market Paperback. Book Condition: New. Brand new. We distribute directly for the publisher. We prove a parabolic Harnack inequality for a centered sub-Laplacian $L$ on a connected Lie group $G$ of polynomial volume growth by using ideas from Homogenisation theory and by adapting the method of Krylov and Safonov. We use this inequality to obtain a Taylor formula for the heat functions and thus we also obtain Harnack inequalities for their space and time derivatives. We characterise the harmonic functions which grow polynomially. We obtain Gaussian estimates for the heat kernel and estimates similar to the classical Berry-Esseen estimate. Finally, we study the associated Riesz transform operators. If $L$ is not centered, then we can conjugate $L$ by a convenient multiplicative function and obtain another centered sub-Laplacian $L_C$. Thus our results also extend to non-centered sub-Laplacians. Bookseller Inventory # 1005250053

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Georgios K. Alexopoulos
Published by Amer Mathematical Society (2002)
ISBN 10: 0821827642 ISBN 13: 9780821827642
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Book Description Amer Mathematical Society, 2002. Mass Market Paperback. Book Condition: New. Bookseller Inventory # DADAX0821827642

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Georgios K. Alexopoulos
ISBN 10: 0821827642 ISBN 13: 9780821827642
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Book Description Book Condition: Brand New. Book Condition: Brand New. Bookseller Inventory # 97808218276421.0

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