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

MathSciNet review:
0315517

Full-text PDF Free Access

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]**Allen Devinatz,*Toeplitz operators on 𝐻² spaces*, Trans. Amer. Math. Soc.**112**(1964), 304–317. MR**0163174**, 10.1090/S0002-9947-1964-0163174-9**[2]**Edgar Raymond Lorch,*Spectral theory*, University Texts in the Mathematical Sciences, Oxford University Press, New York, 1962. MR**0136967****[3]**J. W. Moeller,*On the differentiability and integrability of exponential sums*, J. Math. Anal. Appl.**36**(1971), 301–307. MR**0281925****[4]**H. R. Pousson,*Systems of Toeplitz operators on 𝐻². II*, Trans. Amer. Math. Soc.**133**(1968), 527–536. MR**0227793**, 10.1090/S0002-9947-1968-0227793-7**[5]**M. Rabindranathan,*On the inversion of Toeplitz operators*, J. Math. Mech.**19**(1969/1970), 195–206. MR**0251558****[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]**Harold Widom,*Inversion of Toeplitz matrices. II*, Illinois J. Math.**4**(1960), 88–99. MR**0130572**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
47E05,
34G05,
47B35

Retrieve articles in all journals with MSC: 47E05, 34G05, 47B35

Additional Information

DOI:
http://dx.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