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We're stuck on the following question in a problem relevant to a physics paper on AdS/CFT that we are working on. Given a Fredholm equation of second kind with the form $f+int_D K f\,dx = 0$, where $\int_D K f\,dx$ is not a contraction and $D$ is compact, what are some of the general cases in which $f=0$ is the unique solution?

Alternatively, what restrictions on $K$ does one have to put to obtain a unique solution?

We're stuck on the following question in a problem relevant to a physics paper on AdS/CFT that we are working on. Given a Fredholm equation of second kind with the form $f$+$\int_D K f\,dx = 0$, where $\int_D K f\,dx$ is not a contraction and $D$ is compact, what are some of the general cases in which $f=0$ is the unique solution?

Alternatively, what restrictions on $K$ does one have to put to obtain a unique solution?

We're stuck on the following question in a problem relevant to a physics paper on AdS/CFT that we are working on. Given a Fredholm equation of second kind with the form f+int_D K f dx = 0, where \int_D K fdx is not a contraction and D is compact, what are some of the general cases in which f=0 is the unique solution?

Alternatively, what restrictions on K does one have to put to obtain a unique solution?

Thanks, Ning

We're stuck on the following question in a problem relevant to a physics paper on AdS/CFT that we are working on. Given a Fredholm equation of second kind with the form $f+int_D K f\,dx = 0$, where $\int_D K f\,dx$ is not a contraction and $D$ is compact, what are some of the general cases in which $f=0$ is the unique solution?

Alternatively, what restrictions on $K$ does one have to put to obtain a unique solution?