A new family of kernels for Support Vector Machine is proposed by taking the dot product of two function vectors. These kernels are proved to be admissible support vector kernels, and the dot product function in the kernels can be selected as the polynomial, the Gaussian radial basis function, the exponential radial basis function, the wavelet function, the autocorrelation wavelet function, the probability function, etc. Experiments show the feasibility of the proposed kernels for pattern recognition. The dual-tree complex wavelet is used to extract invariant features for recognizing similar handwritten numerals, and the recognition rate is about 99.50% for a training data set of 800 samples and a testing data set of 400 samples. It is also possible to apply the proposed kernels to function regression.