[線代] inner product and Kernel

[asdc20 (asdc20)]

Inner product:

Consider the set of all integrable functions on [a,b].  Determine whether

                        <x,y>=x(a)y(a)

is a suitable inner product.


Kernel:

Consider the integral operator L on C([a,b];R) defind by

                 Lx=∫K(γ,t)x(γ)dγ (integral form a to b)


where K is is a given continuous function, called Kernel of L. Show that L is
a linear operator.



先謝謝各位



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◆ From: 129.7.255.32
※ 編輯: asdc20          來自: 129.7.255.32         (02/05 19:55)
→ willydp     :1. No, an inner product should be p.d.
→ willydp     :2. L is linear, bounded, and compact. It is easy.
→ herstein    :因為積分線性運算