Three Problems on Trigonometric Sums
Tóm tắt
Let Λ ⊂ ℝn be a uniformly discrete set and let CΛ be the vector space consisting of all mean periodic functions whose spectrum is simple and contained in Λ. If Λ is a gentle set then for every f ∈ CΛ we have f(x) = O(ωΛ(x)) as |x| → ∞ and ωΛ(x) can be estimated (Theorem 4.1). This line of research was proposed by Jean-Pierre Kahane in 1957.
Tài liệu tham khảo
Grepstad, S., Lev, N.: Sets of bounded discrepancy for multi-dimensional irrational rotation. Geometric and Functional Analysis, 25(1), 87–133 (2015)
Grepstad, S., Lev, N.: Multi-tiling and Riesz bases. Advances in Mathematics, 252, 1–6 (2014)
Grepstad, S., Lev, N.: Universal sampling, quasicrystals and bounded remainder sets. Comptes Rendus Mathematique, 352(7–8), 633–638 (2014)
Kahane, J. P.: Sur les fonctions moyenne-périodiques bornées. Ann. Inst. Fourier, 7, 293–314 (1957)
Matei, B., Meyer, Y.: Simple quasi crystals are sets of stable sampling. Complex Variables and Elliptic Equations, 55(8–10), 947–964 (2010)
Meyer, Y.: Mean periodic functions and irregular sampling. Det Kongelige Norske Videnskabers Selskab Skrifter, (2018)
Meyer, Y.: Localization of trigonometric sums. Submitted to Det Kongelige Norske Videnskabers Selskab Skrifter
Meyer, Y.: Théorie L p des sommes trigonométriques apériodiques. Ann. Inst. Fourier, 24(4), 189–211 (1974)