Hermite函数的原函数的平方可积性

The Square Integrability of the Antiderivative of Hermite Function

讨论了n阶Hermite函数的"变上限积分"型原函数在R=(-∞,+∞)上的平方可积性,证明了当n为偶数时这种原函数不是平方可积,而当n为奇数时这种原函数是平方可积的,并给出了n为奇数时原函数的L^2(R)范数的上界.

We discuss the square integrability of the antiderivative of Hermite function of degree n which has the form of integral with variable upper limit over R=(-∞,+∞).We prove that when n is even the antiderivative is not square integrable,while when n is odd the antiderivative is square integrable,and obtain an upper bound of the norm in L2(R)for the antiderivative when n is odd.