- #1

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Three linear operators defined on this space are [tex] A=d/dt [/tex] and [tex]B=t[/tex] and [tex]C=1[/tex] so that [tex]Af=df/dt[/tex] and [tex]Bf=tf[/tex] and [tex]Cf=f[/tex]

I need to find the eigenvalues of these operators:

For A:

[tex]\frac{df}{dt} = \lambdaf[/tex]

[tex]\frac{d ln(f)}{dt} = \lambda [/tex]

[tex]d(ln(f))=\lambda dt+c[/tex]

[tex]f=ce^{\lambda t}[/tex]

So the eigenvalues for A are continuous and can be any real number.

For B:

[tex]tf=\lambda f[/tex]

[tex]\lambda =t [/tex]

The eigenvalues are the variable t?

For B;

[tex]Cf=f=\lambda f[/tex]

The eigenvalue is 1.

Confused about B.