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Spectral analysis of finite convolution operators with matrix kernels. (English) Zbl 0436.47043


MSC:

47Gxx Integral, integro-differential, and pseudodifferential operators
47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
45P05 Integral operators

Citations:

Zbl 0298.47027
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Full Text: DOI

References:

[1] Carathéodory, C.: Theory of Functions, Vol. II. New York, Chelsea 1954. · Zbl 0055.30301
[2] Frankfurt, R.: Spectral Analysis of Finite Convolution Operators. Trans. Amer. Math. Soc. 214 (1975), 279–301. · Zbl 0322.47030 · doi:10.1090/S0002-9947-1975-0397481-9
[3] Frankfurt, R.: On the Unicellularity of Finite Convolution Operators. Ind. U. Math. J. 26 (1977), 223–232. · Zbl 0364.45005 · doi:10.1512/iumj.1977.26.26016
[4] Frankfurt, R. and Rovnyak, J.: Finite Convolution Operators. J. Math. Anal. Appl. 49 (1975), 347–374. · Zbl 0298.47027 · doi:10.1016/0022-247X(75)90185-7
[5] Frankfurt, R. and Rovnyak, J.: Recent Results and Unsolved Problems on Finite Convolution Operators. Linear Spaces and Approximation. Basel, Birkhauser Verlag 1978. · Zbl 0379.47036
[6] Hill, L.T.: Spectral Analysis of Finite Convolution Operators with Matrix Kernels. Dissertation, University of Virginia, 1979.
[7] Kalisch,G.K.: On Similarity, Reducing Manifolds, and Unitary Equivalence of Certain Volterra Operators. Ann. of Math. 66 (1957), 481–494. · Zbl 0078.09602 · doi:10.2307/1969905
[8] Muhly, P.S.: Compact Operators in the Commutant of a Contraction. J. Funct. Anal. 8 (1971), 197–224. · Zbl 0225.47007 · doi:10.1016/0022-1236(71)90010-3
[9] Ringrose, J.R.: Super-diagonal Forms for Compact Linear Operators. Proc. Lond. Math. Soc. 12 (1962), 367–384. · Zbl 0102.10301 · doi:10.1112/plms/s3-12.1.367
[10] Sahnovič, L.A.: Spectral Analysis of Operators of the Form Kf = 0 x f(t)k(x)dt. Isv. Akad. Nauk SSSR 22 (1958), 299–308.
[11] Sahnovič, L.A.: Spectral Analysis of Volterra Operators Prescribed in the Vector-function Space L m 2 (0,). Ukrain. Mat. Z 16 (1964), 259–268; Amer. Math. Soc. Trans. 61 (1967), 85–95.
[12] Sz. Nagy, B. and Foias, C.: Harmonic Analysis of Operators on Hilbert Space. New York, North Holland 1970. · Zbl 0201.45003
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