[{"author":[{"full_name":"Wigderson, Avi","last_name":"Wigderson","first_name":"Avi"},{"last_name":"Wigderson","first_name":"Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","full_name":"Wigderson, Yuval"}],"date_updated":"2026-07-14T09:02:39Z","title":"The uncertainty principle: Variations on a theme","article_type":"original","publication_identifier":{"eissn":["1088-9485"],"issn":["0273-0979"]},"day":"04","arxiv":1,"OA_place":"repository","external_id":{"arxiv":["2006.11206"]},"_id":"22175","extern":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2006.11206"}],"quality_controlled":"1","oa_version":"Preprint","scopus_import":"1","volume":58,"citation":{"mla":"Wigderson, Avi, and Yuval Wigderson. “The Uncertainty Principle: Variations on a Theme.” <i>Bulletin of the American Mathematical Society</i>, vol. 58, no. 2, American Mathematical Society, 2021, pp. 225–61, doi:<a href=\"https://doi.org/10.1090/bull/1715\">10.1090/bull/1715</a>.","ieee":"A. Wigderson and Y. Wigderson, “The uncertainty principle: Variations on a theme,” <i>Bulletin of the American Mathematical Society</i>, vol. 58, no. 2. American Mathematical Society, pp. 225–261, 2021.","ama":"Wigderson A, Wigderson Y. The uncertainty principle: Variations on a theme. <i>Bulletin of the American Mathematical Society</i>. 2021;58(2):225-261. doi:<a href=\"https://doi.org/10.1090/bull/1715\">10.1090/bull/1715</a>","ista":"Wigderson A, Wigderson Y. 2021. The uncertainty principle: Variations on a theme. Bulletin of the American Mathematical Society. 58(2), 225–261.","apa":"Wigderson, A., &#38; Wigderson, Y. (2021). The uncertainty principle: Variations on a theme. <i>Bulletin of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/bull/1715\">https://doi.org/10.1090/bull/1715</a>","chicago":"Wigderson, Avi, and Yuval Wigderson. “The Uncertainty Principle: Variations on a Theme.” <i>Bulletin of the American Mathematical Society</i>. American Mathematical Society, 2021. <a href=\"https://doi.org/10.1090/bull/1715\">https://doi.org/10.1090/bull/1715</a>.","short":"A. Wigderson, Y. Wigderson, Bulletin of the American Mathematical Society 58 (2021) 225–261."},"doi":"10.1090/bull/1715","year":"2021","article_processing_charge":"No","publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2021-01-04T00:00:00Z","page":"225-261","type":"journal_article","oa":1,"issue":"2","mathsc":["81S07","43A25","20C15","94A12"],"publication":"Bulletin of the American Mathematical Society","month":"01","status":"public","abstract":[{"lang":"eng","text":"We show how a number of well-known uncertainty principles for the Fourier transform, such as the Heisenberg uncertainty principle, the Donoho–Stark uncertainty principle, and Meshulam’s nonabelian uncertainty principle, have little to do with the structure of the Fourier transform itself. Rather, all of these results follow from very weak properties of the Fourier transform (shared by numerous linear operators), namely that it is bounded as an operator  L1 → L∞, and that it is unitary. Using a single, simple proof template, and only these (or weaker) properties, we obtain some new proofs and many generalizations of these basic uncertainty principles, to new operators and to new settings, in a completely unified way. Together with our general overview, this paper can also serve as a survey of the many facets of the phenomena known as uncertainty principles."}],"date_created":"2026-06-29T10:57:49Z","publisher":"American Mathematical Society","language":[{"iso":"eng"}],"OA_type":"green","intvolume":"        58"},{"page":"409-427","article_type":"original","publication_identifier":{"issn":["0273-0979"]},"day":"01","type":"journal_article","author":[{"first_name":"Vadim","last_name":"Kaloshin","orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"},{"full_name":"Levi, Mark","first_name":"Mark","last_name":"Levi"}],"year":"2008","article_processing_charge":"No","keyword":["Applied Mathematics","General Mathematics"],"publication_status":"published","date_updated":"2021-01-12T08:19:47Z","date_published":"2008-07-01T00:00:00Z","title":"An example of Arnold diffusion for near-integrable Hamiltonians","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":45,"publisher":"American Mathematical Society","abstract":[{"text":"In this paper, using the ideas of Bessi and Mather, we present a simple mechanical system exhibiting Arnold diffusion. This system of a particle in a small periodic potential can be also interpreted as ray propagation in a periodic optical medium with a near-constant index of refraction. Arnold diffusion in this context manifests itself as an arbitrary finite change of direction for nearly constant index of refraction.","lang":"eng"}],"date_created":"2020-09-18T10:48:20Z","doi":"10.1090/s0273-0979-08-01211-1","intvolume":"        45","citation":{"chicago":"Kaloshin, Vadim, and Mark Levi. “An Example of Arnold Diffusion for Near-Integrable Hamiltonians.” <i>Bulletin of the American Mathematical Society</i>. American Mathematical Society, 2008. <a href=\"https://doi.org/10.1090/s0273-0979-08-01211-1\">https://doi.org/10.1090/s0273-0979-08-01211-1</a>.","short":"V. Kaloshin, M. Levi, Bulletin of the American Mathematical Society 45 (2008) 409–427.","mla":"Kaloshin, Vadim, and Mark Levi. “An Example of Arnold Diffusion for Near-Integrable Hamiltonians.” <i>Bulletin of the American Mathematical Society</i>, vol. 45, no. 3, American Mathematical Society, 2008, pp. 409–27, doi:<a href=\"https://doi.org/10.1090/s0273-0979-08-01211-1\">10.1090/s0273-0979-08-01211-1</a>.","ieee":"V. Kaloshin and M. Levi, “An example of Arnold diffusion for near-integrable Hamiltonians,” <i>Bulletin of the American Mathematical Society</i>, vol. 45, no. 3. American Mathematical Society, pp. 409–427, 2008.","apa":"Kaloshin, V., &#38; Levi, M. (2008). An example of Arnold diffusion for near-integrable Hamiltonians. <i>Bulletin of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/s0273-0979-08-01211-1\">https://doi.org/10.1090/s0273-0979-08-01211-1</a>","ista":"Kaloshin V, Levi M. 2008. An example of Arnold diffusion for near-integrable Hamiltonians. Bulletin of the American Mathematical Society. 45(3), 409–427.","ama":"Kaloshin V, Levi M. An example of Arnold diffusion for near-integrable Hamiltonians. <i>Bulletin of the American Mathematical Society</i>. 2008;45(3):409-427. doi:<a href=\"https://doi.org/10.1090/s0273-0979-08-01211-1\">10.1090/s0273-0979-08-01211-1</a>"},"language":[{"iso":"eng"}],"issue":"3","month":"07","status":"public","oa_version":"None","publication":"Bulletin of the American Mathematical Society","quality_controlled":"1","_id":"8510","extern":"1"}]