I have some questions about the definition of splines and in particular periodic splines. So in non periodic case splines are piecewise polynomials of degree $<=m$ which are $m-1$ times differentiable.(I took $m-1$ time differentiability for simplicity) By this definition we can call linear or quadratic polynomials splines of degree 3.
For periodic case we need boundary conditions on some interval$(a,b)$ $s^{(q)}(a)=s^{(q)}(b),q=1...m-1$. Does it mean that periodic splines are piecewise polynomials of degree $m$(not smaller then $m$) or constants?
Is there analogue for truncated polynomials basis in periodic case?