Uniform bounds on biorthogonal functions for real exponentials with an application to the control theory of parabolic equations
Authors:
H. O. Fattorini and D. L. Russell
Journal:
Quart. Appl. Math. 32 (1974), 45-69
MSC:
Primary 42A52; Secondary 93C20
DOI:
https://doi.org/10.1090/qam/510972
MathSciNet review:
510972
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
- Lipman Bers, Fritz John, and Martin Schechter, Partial differential equations, Lectures in Applied Mathematics, Vol. III, Interscience Publishers John Wiley & Sons, Inc. New York-London-Sydney, 1964. With special lectures by Lars Garding and A. N. Milgram. MR 0163043
- Alberto-P. Calderón, Integrales singulares y sus aplicaciones a ecuaciones diferenciales hiperbolicas, Cursos y Seminarios de Matemática, Fasc. 3. Universidad de Buenos Aires, Buenos Aires, 1960 (Spanish). MR 0123834
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. General theory; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1958 original; A Wiley-Interscience Publication. MR 1009162
A. Erdélyi (editor), Bateman manuscript project, Vol. II, McGraw-Hill, New York, 1953
- H. O. Fattorini and D. L. Russell, Exact controllability theorems for linear parabolic equations in one space dimension, Arch. Rational Mech. Anal. 43 (1971), 272–292. MR 335014, DOI https://doi.org/10.1007/BF00250466
S. Kaczmarz and H. Steinhaus, Theorie der Orthogonalreihen, Monografje Matematyczne, Tom VI, Warszawa, 1935
- W. A. J. Luxemburg and J. Korevaar, Entire functions and Müntz-Szász type approximation, Trans. Amer. Math. Soc. 157 (1971), 23–37. MR 281929, DOI https://doi.org/10.1090/S0002-9947-1971-0281929-0
V. J. Mizel and T. I. Seidman, Observation and prediction for the heat equation, II, Report 70–35, Department of Mathematics, Carnegie-Mellon University
- Laurent Schwartz, Étude des sommes d’exponentielles. 2ième éd, Publications de l’Institut de Mathématique de l’Université de Strasbourg, V. Actualités Sci. Ind., Hermann, Paris, 1959 (French). MR 0106383
- W. Sternberg, Über die Gleichung der Wärmeleitung, Math. Ann. 101 (1929), no. 1, 394–398 (German). MR 1512542, DOI https://doi.org/10.1007/BF01454850
- G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
- A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
L. Bers, F. John and M. Schechter, Partial differential equations, Interscience, New York, 1964
A. P. Calderón, Integrales singulares y sus aplicaciones a ecuaciones diferenciales hiperbólicas, Cursos y Seminarios de Matemática, Fasc. 3, Universidad de Buenos Aires, 1960
R. Courant and D. Hilbert, Methods of mathematical physics, Interscience, New York, 1953
N. Dunford and J. T. Schwartz, Linear operators, Part II : Spectral theory, Interscience, New York, 1963
A. Erdélyi (editor), Bateman manuscript project, Vol. II, McGraw-Hill, New York, 1953
H. O. Fattorini and D. L. Russell, Exact controllability theorems for linear parabolic equations in one space dimension, Arch. Rat. Mech. Anal. 4, 272–292 (1971)
S. Kaczmarz and H. Steinhaus, Theorie der Orthogonalreihen, Monografje Matematyczne, Tom VI, Warszawa, 1935
W. A. J. Luxemburg and J. Korevaar, Entire functions and Müntz-Szász type approximation, Trans. Amer. Math. Soc. 156 (1971)
V. J. Mizel and T. I. Seidman, Observation and prediction for the heat equation, II, Report 70–35, Department of Mathematics, Carnegie-Mellon University
L. Schwartz, Etude des sommes d’exponentielles, 2d edition, Hermann, Paris, 1959
W. Sternberg, Über die Gleichung der Warmeleitung, Math. Ann. 101, 394–398 (1929)
G. N. Watson, A treatise on the theory of Bessel functions, 2d edition, Cambridge University Press, Cambridge, 1944
A. Zygmund, Trigonometric series, 2d edition, Cambridge University Press, Cambridge, 1959
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
42A52,
93C20
Retrieve articles in all journals
with MSC:
42A52,
93C20
Additional Information
Article copyright:
© Copyright 1974
American Mathematical Society
