科研之友
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摘要
A theorem of Lorch, Muldoon and Szeg states that the sequence { ⊿ j ㊣,kj ㊣,k+1t ⊿ ＊ ㊣|J ㊣(t)|dt}k=1 ⊿ is decreasing for ㊣%26gt; ⊿ ＊1/2, where J ㊣(t) the Bessel function of the first kind order ㊣ and j ㊣,k its kth positive root. This monotonicity property implies Szeg %26apos;s inequality ⊿ 0xt ⊿ ＊ ㊣J ㊣(t)dt ⊿ ㏑ ㄓ0, when ㊣ ⊿ ㏑ ㄓ ㊣ ⊿ ? 2 and ㊣ ⊿ ? 2 is the unique solution of ⊿ 0j ㊣,2t ⊿ ＊ ㊣J ㊣(t)dt=0.
- 出版日期1997
