Orthogonality, positive operators, and the frequency-power formulas
Authors:
Ronald A. Skoog and Jan C. Willems
Journal:
Quart. Appl. Math. 29 (1971), 341-361
MSC:
Primary 42A84; Secondary 94A15
DOI:
https://doi.org/10.1090/qam/420126
MathSciNet review:
420126
Full-text PDF Free Access
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Additional Information
J. M. Manley and H. E. Rowe, Some general properties of nonlinear elements. I. General energy relations, Proc. IRE 44, 904–913 (1956)
C. H. Page, Frequency conversion with positive nonlinear resistors, J. Res. Nat. Bur. Standards 56, 179–182 (1956)
P. Penfield, Jr., Frequency-power formulas, Technology Press of M.I.T., Wiley, New York, 1960
R. H. Pantell, General power relationships for positive and negative nonlinear resistive elements, Proc. IRE 46, 1910–1913 (1958)
J. E. Caroll, A simplified derivation of the Manley and Rowe power relationships, J. Elect. Control 6, 359–361 (1959)
P. A. Clavier, On the Manley-Rowe relation, Proc. IRE 47, 1781–1782 (1959)
J. M. Manley and H. E. Rowe, General energy relations in nonlinear reactances, Proc. IRE 47, 2115–2116 (1959)
B. Salzberg, Masers and reactance amplifiers—basic power relations, Proc. IRE 45, 1544–1545 (1957)
- Walter Rudin, Real and complex analysis, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210528
- E. C. Titchmarsh, The theory of functions, Oxford University Press, Oxford, 1958. Reprint of the second (1939) edition. MR 3155290
- A. S. Besicovitch, Almost periodic functions, Dover Publications, Inc., New York, 1955. MR 0068029
- Harald Bohr, Zur theorie der fast periodischen funktionen, Acta Math. 45 (1925), no. 1, 29–127 (German). I. Eine verallgemeinerung der theorie der fourierreihen. MR 1555192, DOI https://doi.org/10.1007/BF02395468
- W. Maak, Fastperiodische Funktionen, Die Grundlehren der mathematischen Wissenschaften, Band 61, Springer-Verlag, Berlin-New York, 1967 (German). Zweite, korrigierte Auflage. MR 0215015
N. N. Bogoliubov, Sur quelques propriétés arithmétiques des presque-périodes, Ann. Chaire Phys. Math. Kiev 4, 185–205 (1939); see also [13] pp. 25–27
B. D. O. Anderson, When do the Manley-Rowe relations really hold?, Proc. IEEE 113, 585–587 (1966)
- Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley and Sons), New York-London, 1962. MR 0152834
- William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0210154
J. C. Willems, The theory of feedback systems, M.I.T. Press, Cambridge, Mass., 1970
- Jan C. Willems and Roger W. Brockett, Some new rearrangement inequalities having application in stability analysis, IEEE Trans. Automatic Control AC-13 (1968), 539–549. MR 0262271, DOI https://doi.org/10.1109/tac.1968.1098999
R. P. O’Shea, A combined frequency-time domain stability criteria. 1, IEEE Trans. Automatic Control. AC-10, 255–261 (1965)
- G. Zames and P. L. Falb, Stability conditions for systems with monotone and slope-restricted nonlinearities, SIAM J. Control 6 (1968), 89–108. MR 0229470
J. M. Manley and H. E. Rowe, Some general properties of nonlinear elements. I. General energy relations, Proc. IRE 44, 904–913 (1956)
C. H. Page, Frequency conversion with positive nonlinear resistors, J. Res. Nat. Bur. Standards 56, 179–182 (1956)
P. Penfield, Jr., Frequency-power formulas, Technology Press of M.I.T., Wiley, New York, 1960
R. H. Pantell, General power relationships for positive and negative nonlinear resistive elements, Proc. IRE 46, 1910–1913 (1958)
J. E. Caroll, A simplified derivation of the Manley and Rowe power relationships, J. Elect. Control 6, 359–361 (1959)
P. A. Clavier, On the Manley-Rowe relation, Proc. IRE 47, 1781–1782 (1959)
J. M. Manley and H. E. Rowe, General energy relations in nonlinear reactances, Proc. IRE 47, 2115–2116 (1959)
B. Salzberg, Masers and reactance amplifiers—basic power relations, Proc. IRE 45, 1544–1545 (1957)
W. Rudin, Real and complex analysis, McGraw-Hill, New York, 1966
E. C. Titchmarsh, The theory of functions, Oxford Univ. Press, Fair Lawn, N. J., 1939
A. S. Besicovitch, Almost periodic functions, Dover, New York, 1954
H. Bohr, Zur Theorie der fast-periodichen Funktionen. I, II, III, Acta Math. 45, 29–127 (1924); ibid. 46, 101–214 (1925); ibid. 47, 237–281 (1926)
W. Maak, Fastperiodische Funktionen, Springer-Verlag, Berlin and New York, 1967
N. N. Bogoliubov, Sur quelques propriétés arithmétiques des presque-périodes, Ann. Chaire Phys. Math. Kiev 4, 185–205 (1939); see also [13] pp. 25–27
B. D. O. Anderson, When do the Manley-Rowe relations really hold?, Proc. IEEE 113, 585–587 (1966)
W. Rudin, Fourier analysis on groups, Interscience, New York, 1967
W. Feller, An introduction to probability theory and its applications, Vol. II, Wiley, New York, 1966.
J. C. Willems, The theory of feedback systems, M.I.T. Press, Cambridge, Mass., 1970
J. C. Willems and R. W. Brockett, Some new rearrangement inequalities having applications in stability analysis, IEEE Trans. Automatic Control AC-13, 539–549
R. P. O’Shea, A combined frequency-time domain stability criteria. 1, IEEE Trans. Automatic Control. AC-10, 255–261 (1965)
G. Zames and P. L. Falb, Stability conditions for systems with monotone and slope-restricted non-linearities, SIAM J. Control. 6, 89–108 (1966)
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Article copyright:
© Copyright 1971
American Mathematical Society
