Notizen: Fieldgradient Two-Center Integrals by the Fourier Convolution Theorem
نویسندگان
چکیده
منابع مشابه
A Note on the Convolution Theorem for the Fourier Transform
In this paper we characterize those bounded linear transformations Tf carrying L1(R1) into the space of bounded continuous functions on R1 , for which the convolution identity T (f ∗ g) = Tf ·Tg holds. It is shown that such a transformation is just the Fourier transform combined with an appropriate change of variable.
متن کاملConvolution and Product Theorem for the Special Affine Fourier Transform
The Special Affine Fourier Transform or the SAFT generalizes a number of well known unitary transformations as well as signal processing and optics related mathematical operations. Unlike the Fourier transform, the SAFT does not work well with the standard convolution operation. Recently, Q. Xiang and K. Y. Qin introduced a new convolution operation that is more suitable for the SAFT and by whi...
متن کاملEvaluation of Two-Center, Two-Electron Integrals.
We present a new analytic treatment of two-electron integrals over two-center integrals including correlation (interelectronic distance) explicitly in the wave function. All the integrals needed for the evaluation of the matrix elements of any diatomic two-electron molecule are obtained as analytic recursion expressions. As an application of this method in molecular physics, we calculate the va...
متن کاملOn the Fresnel Integrals and the Convolution
The Fresnel cosine integral C(x), the Fresnel sine integral S(x), and the associated functions C + (x), C − (x), S + (x), and S − (x) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel cosine integral and its associated functions with x r + and x r are evaluated. The Fresnel cosine integral C(x) is defined by C(x) = 2 π x 0 cos ...
متن کاملOn the uniqueness of the convolution theorem for the fourier transform
This paper shows that members of the fourier transform family are the only linear transforms that have a convolution theorem, that is, that can replace O(N 2) operations of a convolution in a time domain by O(N) operations in a transform domain. Generally, there is an additional cost to compute the transform itself. Our observation is motivated by recent activity in wavelet and subband decompos...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Zeitschrift für Naturforschung A
سال: 1969
ISSN: 1865-7109,0932-0784
DOI: 10.1515/zna-1969-1031