Abstract
In this note we extend the gauge theorem to certain sets of infinite measure provided they are “Small” at infinity. For such sets when the gauge is bounded we show that the Schrödinger-Green Kernel is weakly compact in L’ and compact in Lp for 1<p<∞.
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References
K. L. Chung and K. M. Rao, General Gauge Theorem for Multiplicative Functionals. Trans. A.M.S., 306 (1988) 819–836.
P. J. McKenna and Murali Rao, Lower Bounds for the First Eigen Value of Laplacian. Applicable Analysis 18 (1984) 55–66.
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© 1989 Birkhäuser Boston
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Rao, M.K. (1989). Some Results for Functions of Kato Class in Domains of Infinite Measure. In: Çinlar, E., Chung, K.L., Getoor, R.K., Glover, J. (eds) Seminar on Stochastic Processes, 1988. Progress in Probability, vol 17. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3698-6_15
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DOI: https://doi.org/10.1007/978-1-4612-3698-6_15
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8217-4
Online ISBN: 978-1-4612-3698-6
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