A Normal Monoguy

I've been doing my thesis for a month. I don't have much thing to write lately so here we go. This is my thesis task for this week.

• Replace the function $h(t)=(1+t)^{-k}$ in the $1^{st}$ case by something else.
• Write down the case $\alpha=\beta>0$ which has already been solved. The answer is $||h|| = L^1$-norm upto constance.
• Try $\frac{X_{(0,R)}}{w}$ using any approximation.
• Calculate the matrices.

Why do we study convolution operators?

• There are many applications of convolutions in Physics and engineering. For example, we need convolution operator to compute the work done by electricity? Need more research on this.
• Also $L^2$ spaces are some ways natural. It occurs in lot of areas in science.