The uncertainty principle: Variations on a theme

Quantum smooth uncertainty principles for von Neumann bi-algebras

“…On one hand, our results generalized numbers of uncertainty principles for quantum symmetries in [9,16]. On the other hand, these results are slightly stronger than uncertainty principles for k-Hadamard matrices in [22]. See Theorems 3.9, 3.13, 3.22 and 3.28.…”

“…In [22], A. Wigderson and Y. Wigderson proposed a conjecture on the Wigderson-Wigderson uncertainty principle for the real line R. We give a complete answer to the conjecture, see Theorem 4.3 for details.…”

“…In 2021, A. Wigderson and Y. Wigderson [22] introduced k-Hadamard matrices, as an analogue of discrete Fourier transforms, and they proved various uncertainty principles such as primary uncertainty principles, support uncertainty principles etc. Their work unifies numbers of proofs of uncertainty principles in classical settings.…”

“…The primary uncertainty principle for k-Hadamard matrices plays a key role in [22] and we call this type of uncertainty principle the Wigderson-Wigderson uncertainty principle. We prove the Wigderson-Wigderson uncertainty principle for von Neumann k-bi-algebras in Theorems 2.8 and for subfactors in Theorem 3.…”

An uncertainty principle for distributions, and the support of an alpha-cosine transform

“…The relationship between the zero set sizes of a function and its spectrum is one of several flavors of uncertainty principles in harmonic analysis. For a thorough exposition of this broad area, see [14], or [41] for a more recent overview. A typical support-type uncertainty principle asserts that the supports, or possibly the complements of the zero sets, of a function and its spectrum cannot both be too small.…”