References

  1. Andersen N.B., de Jeu M. Real Paley-Wiener theorems and local spectral radius formulas. Trans. Amer. Math. Soc. 2010, 362 (7), 3613-3640. doi: 10.1090/S0002-9947-10-05044-0
  2. Chen Q.H., Li L.Q., Ren G.B. Generalized Paley-Wiener theorems. Int. J. Wavelets Multiresolut Inf. Process 2012, 10 (2), 1250020. doi: 10.1142/S0219691312500208
  3. Chettaoui C., Othmani Y., Trimèchi K. On the range of the Dunkl transform on $\mathbb R$. Math. Sci. Res. J. 2004, 8 (3), 85-103.
  4. Dineen S. Complex analysis on infinite-dimensional spaces. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1999.
  5. Edwards R.E. Functional Analysis: Theory and Applications. Dover Publ., New York, 2011.
  6. Fu Y.X., Li L.Q. Real Paley-Wiener theorems for the Clifford Fourier transform. Sci. China Math. 2014, 57 (11), 2381-2392. doi:10.1007/s11425-014-4838-7
  7. Gardner R.J. Geometric Tomography. Cambridge University Press, New York, 1995.
  8. Grasela K. Ultraincreasing distributions of exponential type. Univ. Iagel. Acta Math. 2003, 41, 245-253.
  9. Khrennikov A.Yu., Petersson H. A Paley-Wiener theorem for generalized entire functions on infinite-dimensional spaces. Izv. Math. 2001, 65 (2), 403-424. doi: 10.1070/im2001v065n02ABEH000332 (translation of Izv. Ross. Akad. Nauk Ser. Mat. 2001, 65 (2), 201-224. doi: 10.4213/im332 (in Russian))
  10. Komatsu H. An Introduction to the Theory of Generalized Functions. University Publ., Tokyo, 2000.
  11. Komatsu H. Ultradistributions I. Structure theorems and a characterization. J. Fac. Sci. Tokyo, Sec. IA 1973, 20, 25-105.
  12. Lopushansky O.V., Sharyn S.V. Polynomial ultradistributions on cone $\mathbb R^d_+$. Topology 2009, 48 (2-4), 80-90. doi:10.1016/j.top.2009.11.005
  13. Mitjagin B.S. Nuclearity and other properties of spaces of type $S$. Trudy Moscow. Math. Sci. 1960, 9, 317-328. (in Russian)
  14. Nikol'skii S.M. Approximation of Functions of Several Variables and Imbedding Theorems. Springer-Verlag, Berlin, 1975. doi: 10.1007/978-3-642-65711-5
  15. Musin I.Kh. Paley-Wiener type theorems for functions analytic in tube domains. Math. Notes 1993, 53 (4), 418-423. doi: 10.1007/BF01210225 (translation of Mat. Zametki 1993, 53 (4), 92-100. (in Russian))
  16. Paley R., Wiener N. Fourier Transform in the Complex Domain. Amer. Math. Soc., Providence RI, 1934.
  17. Proshkina A. Paley-Wiener's Type Theorems for Fourier Transforms of Rapidly Decreasing Functions. Integral Transforms Spec. Funct. 2002, 13 (1), 39-48. doi: 10.1080/10652460212887
  18. Sharyn S.V. The Paley-Wiener theorem for Schwartz distributions with support on a half-line. J. Math. Sci. 1999, 96 (2), 2985-2987. doi: 10.1007/BF02169692 (translation of Mat. Metodi Fiz.-Mekh. Polya 1997, 40 (4), 54-57. (in Ukrainian))
  19. Smirnov A.G. On topological tensor products of functional Frechet and DF spaces. Integral Transforms Spec. Funct. 2009, 20 (3-4), 309-318. doi: 10.1080/10652460802568150
  20. Tuan V.K., Zayed A.I. Paley-Wiener-Type Theorems for a Class of Integral Transforms. J. Math. Anal. Appl. 2002, 266 (1), 200-226. doi: 10.1006/jmaa.2001.7740
  21. Vinnitskii B.V., Dilnyi V.N. On generalization of Paley-Wiener theorem for weighted Hardy spaces. Ufa Math. J. 2013, 5 (3), 30-36. doi: 10.13108/2013-5-4-30 (translation of Ufa Math. Zh. 5 (4), 31-37. (in Russian))
  22. Waphare B.B. A Paley-Wiener type theorem for the Hankel type transform of Colombeau type generalized functions. Asian J. Current Engineering and Maths 2012, 1 (3), 166-172.
  23. Zharinov V.V. Compact families of locally convex topological vector spaces, Fréchet-Schwartz and dual Fréchet-Schwartz spaces. Russian Math. Surveys 1979, 34 (4), 105-143. doi: 10.1070/RM1979v034n04ABEH002963 (translation of Uspekhi Mat. Nauk 1979, 34 (4), 97-131. (in Russian))

Refbacks

  • There are currently no refbacks.


Creative Commons License
The journal is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported.