Bochner–Minlos Theorem and Quaternion Fourier Transform

DOI10.1007/978-3-0348-0603-9_6zbMath1273.30043OpenAlexW122076865MaRDI QIDQ2847057

Kit Ian Kou, Svetlin G. Georgiev, Wolfgang Sprössig, João Pedro Morais

Publication date: 4 September 2013

Published in: Quaternion and Clifford Fourier Transforms and Wavelets (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-0348-0603-9_6

zbMATH Keywords

quaternion Fourier transformBochner-Minlos theoremquaternion analysispositive definite measure

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Positive definite functions in one variable harmonic analysis (42A82)

Related Items (12)

Uncertainty principle for measurable sets and signal recovery in quaternion domains ⋮ Tighter uncertainty principles based on quaternion Fourier transform ⋮ Asymptotic behaviour of the quaternion linear canonical transform and the Bochner-Minlos theorem ⋮ On uncertainty principle for quaternionic linear canonical transform ⋮ Donoho-Stark's uncertainty principle for the quaternion Fourier transform ⋮ Envelope detection using generalized analytic signal in 2D QLCT domains ⋮ Plancherel theorem and quaternion Fourier transform for square integrable functions ⋮ Uncertainty principles associated with quaternionic linear canonical transforms ⋮ Bochner-Minlos theorem in the frame of real Clifford algebras ⋮ Krein reproducing kernel modules in Clifford analysis ⋮ Bochner–Minlos Theorem and Quaternion Fourier Transform ⋮ Herglotz's theorem and quaternion series of positive term

Cites Work

• Clifford Fourier transformation and uncertainty principle for the Clifford geometric algebra \(\mathrm{Cl}_{3,0}\)
• Clifford Fourier transform on multivector fields and uncertainty principles for dimensions \(n=2\pmod 4\) and \(n=3\pmod 4\)
• Solutions of integral and integro-differential equation systems by using differential transform method
• Quaternion Fourier transform on quaternion fields and generalizations
• The Clifford-Fourier transform
• Bochner–Minlos Theorem and Quaternion Fourier Transform
• Hypercomplex Fourier Transforms of Color Images
• Quaternionic ψ-hyperholomorphic functions, singular integral operators and boundary value problems I. ψ-hyperholomorphic function theory
• Quaternionic ψ-hyperholomorphic functions, singular integral operators and boundary value problems II. algebras of singular lntegral operators and riemann type boundary value problems
• Real Quaternionic Calculus Handbook
• Efficient implementation of quaternion Fourier transform, convolution, and correlation by 2-D complex FFT
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