All questions with tag [math: adjoint-operators]


eigenfunctions of the adjoint of an operator

If the eigenfunctions of a straight driver are recognized, exists a means to compute the eigenfunctions of the equivalent adjoint driver based upon the well-known eigenfunctions? To put it simply, what is the relationship in between the eigenfunctions of a driver and also its adjoint? Many thanks!
2022-07-20 01:28:23

Eigenvalues of compact operators and his adjoint.

Let $T: H \to H$ be a portable driver with $H$ a Hilbert room. Allow after that $\lambda \neq 0$ be an eigenvalue of $T$ with eigenfunction $v$. Is after that $\lambda$ an eigenvalue for the adjoint $T^*$ either? Is after that $v$ an eigenfunction for $T^*$? I recognize the above declarations fall short for $\lambda = 0$ and also the counte...
2022-07-07 02:36:50

Exponential Law for based spaces

I understand most individuals operate in "convenient categories" where this is not a concern. In the majority of topology publications there is an evidence of the reality that there is an all-natural homeomorphism of function rooms (with the portable - open geography) : $$F(X\times Y,Z)\cong F(X,F(Y,Z))$$ when $X$ is Hausdorff and als...
2022-06-04 20:38:17