Toeplitz operators and differential equations on a half-line

Author:
J. W. Moeller

Journal:
Proc. Amer. Math. Soc. **36** (1972), 531-534

MSC:
Primary 47E05; Secondary 34G05, 47B35

DOI:
https://doi.org/10.1090/S0002-9939-1972-0315517-0

MathSciNet review:
0315517

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a separable Hilbert space, let denote bounded linear operators from into , and let represent the set of all functions in whose first *n* derivatives belong to . Suppose further that the space is equipped with an inner product inherited from . The main result of this note states that the differential operator

**[1]**A. Devinatz,*Toeplitz operators on**spaces*, Trans. Amer. Math. Soc.**112**(1964), 304-317. MR**29**#477. MR**0163174 (29:477)****[2]**E. R. Lorch,*Spectral theory*, University Texts in the Math. Sci., Oxford Univ. Press, New York, 1962. MR**25**#427. MR**0136967 (25:427)****[3]**J. W. Moeller,*On the differentiability and integrability of exponential sums*, J. Math. Anal. Appl.**36**(1971), 301-307. MR**0281925 (43:7639)****[4]**H. R. Pousson,*Systems of Toeplitz operators on*. II, Trans. Amer. Math. Soc.**133**(1968), 527-536. MR**37**#3377. MR**0227793 (37:3377)****[5]**M. Rabindranathan,*On the inversion of Toeplitz operators*, J. Math. Mech.**19**(1969/70), 195-206. MR**40**#4785. MR**0251558 (40:4785)****[6]**M. Rosenblum,*Self-adjoint Toeplitz operators*, Summer Institute on Spectral Theory and Statistial Mechanics (Brookhaven National Laboratory), Upton, New York, 1965, pp. 135-157.**[7]**H. Widom,*Inversion of Toeplitz matrices*. II, Illinois J. Math.**4**(1960), 88-99. MR**24**#A432. MR**0130572 (24:A432)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0315517-0

Keywords:
Separable Hilbert space,
differential operator,
Laguerre function,
Toeplitz operator

Article copyright:
© Copyright 1972
American Mathematical Society