Cordial Volterra integral equations. II. (English) Zbl 1194.65152
Summary: We study the mapping properties and spectra of the (cordial) Volterra integral operators of the form \((V_{\varphi,a},u)(t)=\int^t_0 t^{-1}\varphi(t^{-1}\varphi(t^{-1}s)a(t,s)u(s)\,ds\), \(0\leq t\leq T\), where \(\varphi\in L^1(0, 1)\), \(a\in C^m\) \((0\leq s\leq t\leq T)\), \(m \geq 0\). Also polynomial collocation methods for the solving the (cordial) Volterra integral equation \(\mu u = V_{\varphi, a}u + f\) is examined. Here \(\mu\) is real or complex parameter outside the spectrum of \(V_{\varphi, a}\) as an operator in the space \(C[0,T]\).
For part I, cf. Numer. Funct. Anal. Optim. 30, No. 9–10, 1145–1172 (2009; Zbl 1195.45004).
For part I, cf. Numer. Funct. Anal. Optim. 30, No. 9–10, 1145–1172 (2009; Zbl 1195.45004).
MSC:
65R20 | Numerical methods for integral equations |
45A05 | Linear integral equations |
45C05 | Eigenvalue problems for integral equations |
45D05 | Volterra integral equations |
45P05 | Integral operators |
45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
Keywords:
non-compact operators; polynomial collocation; spectrum; (cordial) Volterra integral operatorsCitations:
Zbl 1195.45004References:
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