In this paper recent new approaches to the representation of a positive polynomials as a sum of squares are used in order to compute spectral factorizations of nonnegative multivariable polynomials. In principle this problem is solved due to the positive solution of Hilberts 17th problem by Artin. Unfortunately Artins result is not constructive and the denominator polynomials arising have no sp...

LEMMA L 1 When Kp< oo, then &fis a continuous (bounded) linear transformation with both domain and range Lp( — <*> , oo ), and § 2 / = — ƒ. LEMMA 2. Whenf(t)ÇzLi(— <*>, oo), then §ƒ exists for almost all x in ( — oo , co ), but does not necessarily belong to Li(a, b), where a, b are arbitrary numbers(— oo ^a<b^ oo) ; however (l+x)~\ &f\ÇzLi(— oo , co) when 0<q<l. When f and ^f belong to Li(— oo...

The continuum hypothesis (CH) is one of and if not the most important open problems in set theory, one that is important for both mathematical and philosophical reasons. The general problem is determining whether there is an infinite set of real numbers that cannot be put into one-to-one correspondence with the natural numbers or be put into one-to-one correspondence with the real numbers respe...

in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.

in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.