We consider the set
S r,n of periodic (with period 1) splines of degree
r with deficiency 1 whose nodes are at
n equidistant points
xi=i /
n. For
n-tuples
y = (
y0, ... ,
yn-1), we take splines
s r,n (
y,
x) from
S r,n solving the interpolation problem
$$s_{r,n} (y,t_i ) = y_i,$$
where
t i =
x i if
r is odd and
t i is the middle of the closed interval [
x i ,
x i+1 ] if
r is even. For the norms
L r,n * of the operator
y →
s r,n (
y,
x) treated as an operator from
l1 to
L1 [0, 1] we establish the estimate
$$L_{r,n}^ * = frac{4}{{pi ^2 n}}log min(r,n) + Oleft( {frac{1}{n}} right)$$
with an absolute constant in the remainder. We study the relationship between the norms
L r,n * and the norms of similar operators for nonperiodic splines.