Abstract
We establish a trace for nuclear operators on L p, this trace generalize a formula already known in the L 2 case. To prove this we first show a characterization of nuclear operators in the L p setting. As a corollary a formula for the trace of pseudo-differential operators on L p is obtained.
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References
C. Brislawn, Kernels of trace class operators, Proc. Amer. Math. Soc. 104 (1988), 1181–1190.
C. Brislawn, Traceable integral kernels on countably generated measure spaces, Pacific J. Math. 150(2) (1991), 229–240.
J. L. Doob, Stochastic Processes, John Wiley & Sons, 1953.
J. Du and M. W. Wong, A trace formula for Weyl transforms, Approx. Theory Appl. 16(1) (2000), 41–45.
I. Gohberg, S. Goldberg and N. Krupnik, Traces and Determinants of Linear Operators, Birkhäuser, 2001.
H. Hogbe-Nlend and V. B. Moscatelli, Nuclear and Conuclear Spaces, North-Holland, 1981.
M. Reed and B. Simon, Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness, Academic Press, 1975.
B. Simon, Trace Ideals and Their Applications, Cambridge University Press, 1979.
E. M. Stein. Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970.
E. M. Stein, Harmonic Analysis, Princeton University Press, 1993.
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© 2009 Birkhäuser Verlag Basel/Switzerland
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Delgado, J. (2009). A Trace Formula for Nuclear Operators on L p . In: Schulze, BW., Wong, M.W. (eds) Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations. Operator Theory: Advances and Applications, vol 205. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0198-6_10
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DOI: https://doi.org/10.1007/978-3-0346-0198-6_10
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0346-0197-9
Online ISBN: 978-3-0346-0198-6
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