All Questions

There exist a "standard" or canonical way to construct a real valued function whose Mellin transform has a prescribed set of zeroes? Clearly for some set of zeroes this could be impossible ...

I'm looking for references which derive the Lagrange inversion formula, given below (in bold), for the Taylor series coefficients of the compositional inverse of a function $f$ analytic at the origin ...

Consider the following integral equation: $$\int_0^\infty K(t,y)\phi(t,x)dt=0$$ Here, $K(t,y)$ is a trigonometric kernel and $\phi(t,x)$ is monotonic wrt $x$ ( for fixed $t$). I want to find the ...

Let $I=(0,1]$ and $T=\{(x,y)\in I^2;x\geq y\}$. If functions $f:I\to\mathbb R$ and $w:T\to\mathbb R$ are analytic, is the function $A_wf:I\to\mathbb R$, $$ A_wf(y)=\int_y^1\frac{f(x)w(x,y)}{\sqrt{x^2-...