Bohr-Favard Inequalities
If 
has no spectrum in 
, then
(Bohr 1935). A related inequality states that if
is the class of functions such that
are absolutely continuous and
, then
(Northcott 1939). Further, for each value of
, there is always a function 
belonging to and not identicallyzero, for which the above inequality becomes an equality (Favard 1936). These inequalities are discussed in Mitrinovic et al. (1991).
References
Bohr, H. ``Ein allgemeiner Satz über die Integration eines trigonometrischen Polynoms.'' Prace Matem.-Fiz. 43, 1935. Favard, J. ``Application de la formule sommatoire d'Euler à la démonstration de quelques propriétés extrémales des intégrale des fonctions périodiques ou presquepériodiques.'' Mat. Tidsskr. B, 81-94, 1936. [Reviewed in Zentralblatt f. Math. 16, 58-59, 1939.] Mitrinovic, D. S.; Pecaric, J. E.; and Fink, A. M. Inequalities Involving Functions and Their Integrals and Derivatives. Dordrecht, Netherlands: Kluwer, pp. 71-72, 1991. Northcott, D. G. ``Some Inequalities Between Periodic Functions and Their Derivatives.'' J. London Math. Soc. 14, 198-202, 1939. Tikhomirov, V. M. ``Approximation Theory.'' In Analysis II. Convex Analysis and Approximation Theory (Ed. R. V. Gamkrelidze). New York: Springer-Verlag, pp. 93-255, 1990.
- Euler Parameters
- Euler-Poincaré Characteristic
- Euler Polyhedral Formula
- Euler Polynomial
- Euler Polynomial Identity
- Euler Power Conjecture
- Euler Product
- Euler Pseudoprime
- Euler Quartic Conjecture
- Euler's 6n+1 Theorem
- Euler's Addition Theorem
- Euler's Circle
- Euler's Conjecture
- Euler's Criterion
- Euler's Displacement Theorem
- Euler's Distribution Theorem
- Euler's Factorization Method
- Euler's Finite Difference Transformation
- Euler's Graeco-Roman Squares Conjecture
- Euler's Homogeneous Function Theorem
- Euler's Hypergeometric Transformations
- Euler's Idoneal Number
- Euler's Machin-Like Formula
- Euler's Pentagonal Number Theorem
- Euler's Phi Function