Let A be an mth order n-dimensional tensor, where m, nare some positive integers and N:= m(n−1).Then A is called a Hankel tensor associated with a vector v\in {?}^{N+\mathrm{1}} if A_{\sigma }=v_k for each k= 0, 1, …,Nwhenever σ= (i₁, …,i_m) satisfies i₁ +…+i_m = m+k.We introduce the elementary Hankel tensors which are some special Hankel tensors, and present all the eigenvalues of the elementary Hankel tensors for k= 0, 1, 2. We also show that a convolution can be expressed as the product of some third-order elementary Hankel tensors, and a Hankel tensor can be decomposed as a convolution of two Vandermonde matrices following the definition of the convolution of tensors. Finally, we use the properties of the convolution to characterize Hankel tensors and (0,1) Hankel tensors.