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1.
Roman Badora 《Aequationes Mathematicae》1992,43(1):72-89
LetX be a locally compact abelian group and let a compact groupG act onX. We find solutionsf: X inL(X) of the following functional equation:
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2.
In this paper, assuming a certain set-theoretic hypothesis, a positive answer is given to a question of H. Kraljevi, namely it is shown that there exists a Lebesgue measurable subsetA of the real line such that the set {c R: A + cA contains an interval} is nonmeasurable. Here the setA + cA = {a + ca: a, a A}. Two other results about sets of the formA + cA are presented. 相似文献
3.
B. P. Duggal 《Rendiconti del Circolo Matematico di Palermo》2007,56(3):317-330
A Banach space operatorT ɛB(X) is polaroid,T ɛP, if the isolated points of the spectrum ofT are poles of the resolvent ofT. LetPS denote the class of operators inP which have have SVEP, the single-valued extension property. It is proved that ifT is polynomiallyPS andA ɛB(X) is an algebraic operator which commutes withT, thenf(T+A) satisfies Weyl’s theorem andf(T
*+A
*) satisfiesa-Weyl’s theorem for everyf which is holomorphic on a neighbourhood of σ(T+A). 相似文献
4.
H. Haruki 《Aequationes Mathematicae》1990,40(1):271-280
The purpose of this paper is to solve the following Pythagorean functional equation:(e
p(x,y)
)
2
) = q(x,y)
2
+ r(x, y)
2, where each ofp(x,y), q(x, y) andr(x, y) is a real-valued unknown harmonic function of the real variablesx, y on the wholexy-planeR
2.The result is as follows. 相似文献
5.
Answering a question of Z. Daróczy we show that there are positive sequences
n satisfying the recursion
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