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On the discrepancies between POD and Fourier modes on aperiodic domains
The application of Fourier analysis in combination with the Proper Orthogonal Decomposition (POD) is investigated. In this approach to turbulence...
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Boundedness of Fourier Multipliers on Fundamental Domains of Lattices
This short paper is an overview of my research about...
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On Eigenmeasures Under Fourier Transform
Several classes of tempered measures are characterised that are eigenmeasures of the Fourier transform, the latter viewed as a linear operator on...
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Multi-parameter Maximal Fourier Restriction
The main result of this note is the strengthening of a quite arbitrary a priori Fourier restriction estimate to a multi-parameter maximal estimate of...
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Conditioning of Fourier sums on a quadratic curve
The stability property of representations of the Fourier sums on a quadratic curve is measured through a condition number. We analyze the...
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Local behaviors of Fourier expansions for functions of limited regularities
Based on the explicit formula of the pointwise error of Fourier projection approximation and by applying van der Corput-type Lemma, optimal...
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Fourier Series
At this point, we will consider the major technique for solving standard boundary value equations. Consider, for example, the heat equation.
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Fourier Series
In this chapter we consider the representations of functions in the form of series in trigonometric functions. This approach will be used for solving...
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A double Fourier sphere method for d-dimensional manifolds
The double Fourier sphere (DFS) method uses a clever trick to transform a function defined on the unit sphere to the torus and subsequently...
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Fourier matrices and Fourier tensors
The Fourier matrix is fundamental in discrete Fourier transforms and fast Fourier transforms. We generalize the Fourier matrix, extend the concept of...
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On the Computation of the SVD of Fourier Submatrices
Contiguous submatrices of the Fourier matrix are known to be ill-conditioned. In a recent paper in SIAM review A. Barnett has provided new bounds on...
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Quantitative Uncertainty Principles for the Canonical Fourier—Bessel Transform
The aim of this paper is to establish an extension of quantitative uncertainty principles and an algorithm for signal recovery about the essential...
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A note on Fourier restriction and nested Polynomial Wolff axioms
This note records an asymptotic improvement on the known L p range for the Fourier restriction conjecture in high dimensions. This is obtained by...
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On interpretation of Fourier coefficients of Zagier type lifts
Jeon, Kang, and Kim defined the Zagier lifts between harmonic weak Maass forms of negative integral weights and half integral weights. These lifts...
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Local Extension Estimates for the Hyperbolic Hyperboloid in Three Dimensions
We establish Fourier extension estimates for compact subsets of the hyperbolic hyperboloid in three dimensions via polynomial partitioning.
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A Necessary Condition for HK-Integrability of the Fourier Sine Transform Function
The paper is concerned with integrability of the Fourier sine transform function when f ∈ BV 0 (ℝ), where BV 0 (ℝ) is the space of bounded variation...
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Fourier Transform
An integral transform of a function f(x) defined on (a, b) has the form $$I(f)\equiv...
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Quaternion Hyperbolic Fourier Transforms and Uncertainty Principles
The present study introduces the two-sided and right-sided Quaternion Hyperbolic Fourier Transforms (QHFTs) for analyzing two-dimensional...
