A modification of the Wiener-Hopf method for this type of problems is described in <A HREF="https://link.springer.com/article/10.1007%2FBF01202095">Convolution equations on finite intervals and factorization of matrix functions</A> and in <A HREF="https://idp.springer.com/authorize/casa?redirect_uri=https://link.springer.com/article/10.1007/s00020-003-1281-5&casa_token=3ELwfCwsgVMAAAAA:TcFwX3iDyVOcoAY90Zt4UshieiiUhq185Xppd88x9iST_Qx-QDSzrfqjI9ioeRWRfpFXIuyXAjGPKhjTyQ">Finite interval convolution operators with transmission property.</A>

<sub>[both are behind a paywall, if so desired I can email a copy.]</sub>