An Alternative to Plemelj-Smithies Formulas on Infinite Determinants

✍ Scribed by D.H.U. Marchetti

• Book ID: 102592687
• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 400 KB
• Volume: 117
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1993.1130

✦ Synopsis

An alternative to Plemelj-Smithies formulas for the (p)-regularized quantities (d^{(p)}(K)) and (D^{(p)}(K)) is presented which generalizes previous expressions with (p=1) due to Grothendieck and Fredholm. Global upper bounds for these quantities are also presented. In particular, we prove that

[
\left|d^{(\rho)}(K)\right| \leqslant e^{k|\kappa|_{r}^{r}}
]

holds with (k=\kappa(p) \leqslant k(\infty)=e^{1 / 4\left(1+e^{1 \pi}\right)}) for (p \geqslant 3) which improves a previous estimate yielding (k(p)=e(2+\ln (p-1)) . \quad(1993) Academic Press, Inc.