Boehmians
and related topics
This is a list of papers on Boehmians or related topics. If you know of a paper that is missing from my list, or if you have any other suggestions or corrections, please send a message to piotrm@mail.ucf.edu).
D. Atanasiu
and P. Mikusinski, On the Fourier Transform, Boehmians,
and Distributions, Colloq.
Math., 108 (2007), 263-276.
D. Nemzer, One-Parameter Groups of Boehmians, Bulletin of the Korean Mathematical Society 44 (2007), 419-428.
D. Nemzer, Integrable Boehmians, Fourier Transforms, and Poisson's Summation Formula, Applicable Analysis and Discrete Mathematics 1 (2007), 172-183.
D. Nemzer, Boehmians on the Torus, Bulletin of the Korean Mathematical Society 43 (2006), 831-839.
D. Loonker
and P. K. Banerji, Laplace transform for Integrable
Boehmians, Bull.
Cal. Math. Soc. 98 (5) (2006), 465‑470.
P. K. Banerji and D. Loonker, An Introduction to Boehmains and their Transforms, In the “Proc. of Seventh Annual Conference of SSFA” Pune (India), 7 (2006), 49‑56.
R. Roopkumar, Generalized Radon Transform, Rocky Mountain J. Math., 36 (2006), 1375-1390.
R. Roopkumar, Multiplication of Boehmians, Journal of the Indian Mathematical Society, 72 (2005), 59-66.
D. Loonker and P. K. Banerji, Kontorovich-Lebedev transformation of tempered distribution and tempered Boehmians, J. Rajasthan Acad. Phys. Sci., 4 (2005), 165-172.
D. Nemzer, Lacunary Boehmians, Integral Transforms Spec. Funct., 16 (2005), 451-459.
V. Karunakaran and R. Vembu, On point values of Boehmians, Rocky Mountain J. Math., 35 (2005), 181-193.
V. Karunakaran and R. Roopkumar, Operational Calculus and Fourier Transform on Boehmians, Colloquium Mathematicum, 102 (2005) 21-32.
D. Atanasiu and P. Mikusinski, On the Fourier Transform and the Exchange Property, Internat. J. Math. Math. Sci., 16 (2005), 2579–2584.
J. Burzyk and P.
Mikusinski, Remarks on topological properties of Boehmians,
J. Burzyk and P. Mikusinski, A characterization of distribution of finite order in the space of Boehmians, Integral Transform. Spec. Funct., 16 (2005), 639-646.
P. Mikusinski, Generalized Quotients With Applications In Analysis, Methods Appl. Anal., 10 (2004), 377-386.
P. K. Banerji, D. Loonker, and L. Debnath, Wavelet transforms for integrable Boehmians, J. Math. Anal. Appl., 296 (2004), 473-478.
D. Nemzer, Generalized functions and an extended gap theorem, Indian J. Pure Appl. Math., 35 (2004), 43-49.
D. Loonker and P. K. Banerji, Wavelet transform for the tempered Boehmians, Hadronic J. Suppl., 18 (2003), 403-410.
R. Roopkumar, On Extension of Fourier Transform, International Journal of Mathematics, Game theory and Algebra, 13 (2003), 465 – 474.
J. Burzyk and P. Mikusinski, A generalization of the construction of a field of quotients with applications in analysis, Int. J. Math. Sci., 2 (2003), 229-236.
P. Mikusinski, Generalized Functions and Convolutions, Cubo Matemática Educacional, 5 (2003), 197-212.
V. Swaminathan and K. Krishnan, The Mellin transform for two spaces of Boehmians, Acta Cienc. Indica Math., 29 (2003), 519-526.
V. Karunakaran and R. Roopkumar, Periodic Beurling Boehmians and Analytic Boehmians, Methods Appl. Anal., 10 (2003), 137-150.
V. Karunakaran and R. Vembu, Boehmians and their Convolution Transforms, Int. J. Math. Game Theory Algebra, 13 (2003), 161-171.
N. V. Kalpakam and S. Ponnusamy, Convolution transform for Boehmians, Rocky Mountain J. Math., 33 (2003), 1353-1378.
V. Karunakaran and R. Vembu, Hilbert transform on periodic Boehmians, Houston J. Math., 29 (2003), 437-452.
R. Roopkumar, Wavelet analysis on a Boehmian space, Int. J. Math. Math. Sci., 15 (2003), 917-926.
V. Karunakaran and V. Baby Thilaga, Laplace transform for vector valued Boehmians. J. Indian Math. Soc. (N.S.) 69 (2002), 1-21.
V. Swaminathan and K.
Krishnan, The Laplace transform of tempered Boehmians,
Acta Cienc. Indica Math., 28 (2002), 365-370.
V. Karunakaran and R. Roopkumar, Boehmians and their Hilbert Transforms, Integral Transform. Spec. Funct., 13 (2002), 131-141.
V. Karunakaran and R. Roopkumar, Ultra Boehmians and their Fourier transforms, Fract. Calc. Appl. Anal., 5 (2002), 181-194.
P. K. Banerji and Deshna Loonker, Generalized Schwartz distribution: the Boehmians, J. Rajasthan Acad. Phys. Sci., 1 (2002), 17-24.
M. Morimoto, Two definitions of Boehmians on the sphere, Progress in analysis, World
Sci. Publishing,
P. Mikusinski and M. Morimoto, Boehmians on the sphere and their spherical harmonic expansions, Fract. Calc. Appl. Anal., 4 (2001), 25-35.
D. Loonker, Boehmians : A Different Concept of Distributions, In “Proceedings of the International Conference
on the Works of Srinivasa Ramanujan”,
Eds. Chandrashekar Adiga
and D. D. Somashekra, pp.161‑176, Dept. of
Studies in Mathematics, University of Mysore, Mysore (India), May 2001.
D. Loonker, Boehmian Spaces and Wavelets. In “Proceedings of the National Conference on Mathematical Analysis and Applications (NCMAA)”, held at the Himachal Pradesh University, Shimla (India), during Nov. 7‑9 (2000) (ed. R.C. Sharma) (2003), 40 – 51.
V. Karunakaran and N. V. Kalpakam, Boehmians representing measures, Houston J. Math., 26 (2000), 377-386.
P. K. Banerji and D. Loonker,
On the Mellin transform of tempered Boehmians, Politehn.
Univ.
P. Mikusinski, Boehmians on manifolds, Int. J. Math. Math. Sci., 24 (2000), 583-588.
D. Nemzer, A Uniqueness Theorem for Boehmians of Analytic Type, Int. J. Math. Math. Sci.,24 (2000), 501-504.
J. J. Betancor, On
asymptotic behaviours of Boehmians
and Zemanian distributions, Acta
Sci. Math. (
P. Mikusinski and B. A. Pyle, Boehmians on the Sphere, Integral Transform. Spec. Funct. 10 (2000), 93-100.
V. Karunakaran and N.V.Kalpakam, Weierstrass Transform For Boehmians, Int. J. Math. Game Theory Algebra, 11 (2001), 47-65.
V. Karunakaran and N.V.Kalpakam, Hilbert Transform For Boehmians, Integral Transform. Spec. Funct., 9 (2000), 19-36.
V. Karunakaran and T. Venugopal, A New Space for Fourier transform, Integral Transform. Spec. Funct., 9 (2000), 133-148.
V. Karunakaran and N.V.Kalpakam, Boehmians and Fourier transforms, Integral Transform. Spec. Funct., 9 (2000), 197-216.
V. Karunakaran and T. Venugopal, Convolution Transform for Generalized Functions, Integral Transform. Spec. Funct., 8 (1999), 217-232
V. Karunakaran and N.V.Kalpakam,
Boehmians Representing Measures,
D. Nemzer, A Generalized Product, Bull. Inst. Math. Acad. Sinica, 27 (1999), 125-136.
Zayed, Fractional Fourier Transforms of Generalized Functions, Integral Transform. Spec. Funct., 7 (1998), 299-312.
V. Karunakaran and V. B. Thilaga, Plancherel theorem for vector valued functions and Boehmians, Rocky Mountain J. Math. 28 (1998), 1321-1342.
D. Nemzer, A Space of
Convolution Quotients,
P. Mikusinski, On flexibility of Boehmians, Integral Transform. Spec. Funct. 4 (1996), 141-146. (Proceedings of the Conference "Different Aspects of Differentiability II", Gordon and Breach, Yverdon, 1996).
D. Nemzer, A note on generalized logarithms, Bull. Inst. Math. Acad. Sinica 25 (1997), 35-44.
D. Nemzer, The dual space of B(G), Int. J. Math. Math. Sci. 20 (1997), 111-114.
D. Nemzer, Convolution Quotients of Beurling Type, Math. Japonica 43 (1996), 135-142.
J. J. Betancor, M. Linares and J. M. R. Méndez, Ultraspherical transform of summable Boehmians, Math. Japon. 44 (1996), 81-88.
J. J. Betancor, M. Linares and J. M. R. Méndez, The Hankel transform of tempered Boehmians, Boll. Un. Mat. Ital. B (7) 10 (1996), 325-340.
J. J. Betancor, M. Linares and J. M. R. Méndez, The Hankel transform of integrable Boehmians, Appl. Anal. 58 (1995), 367-382.
P. Mikusinski, A. Morse and D. Nemzer, The two-sided Laplace transform for Boehmians, Integral Transform. Spec. Funct. 2 (1994), 219-230.
Zayed and P. Mikusinski, On the extension of the Zak transform, Methods Appl. Anal. 2 (1995), 160-172.
P. Mikusinski and M. L. Mott, The integral wavelet transform of convolutors, Integral Transform. Spec. Funct. 3 (1995), 99-105.
P. Mikusinski, Transforms of Boehmians, Dissertationes Math. (Rozprawy Mat.) 340 (1995), 201-206. (Different aspects of differentiability, Polish Acad. Sci., Warsaw, 1995)
P. Mikusinski and M. Tighiouart, Value of a Boehmian at a point and at infinity, Rocky Mountain J. Math. 24 (1994), 1039-1054.
D. Nemzer, Abelian theorems for transformable Boehmians, Internat. J. Math. Math. Sci. 17 (1994), 489-496.
P. Mikusinski and M. D. Taylor, Toward a unified theory of generalized functions: convergence, Math. Nachr. 161 (1993), 27-43.
P. Mikusinski, The Fourier transform of tempered Boehmians, in Fourier analysis (Orono,
ME, 1992), 303-309,
P. Mikusinski, Tempered Boehmians and ultradistributions, Proc. Amer. Math. Soc. 123 (1995), 813-817.
P. Mikusinski and A. Zayed, An extension of the
Radon transform, in Generalized functions and their applications (
V. Karunakaran and A. Vijayan,
Laplace transforms of generalized functions,
D. Nemzer, The product of a function and a Boehmian, Colloq. Math. 66 (1993), 49-55.
P. Mikusinski and A. Zayed, The Radon transform of Boehmians, Proc. Amer. Math. Soc. 118 (1993), 561-570.
E. R. Dill and P. Mikusinski, Strong Boehmians, Proc. Amer. Math. Soc. 119 (1993), 885-888.
B. Stankovic, Asymptotics of regular convolution quotients, Internat. J. Math. Math. Sci. 15 (1992), 631-634.
D. Nemzer, The Laplace transform on a class of Boehmians, Bull. Austral. Math. Soc. 46 (1992), 347-352.
D. Nemzer, Periodic Boehmians. II, Bull. Austral. Math. Soc. 44 (1991), 271-278.
D. Nemzer, Periodic generalized functions,
P. Mikusinski, Boehmians on open sets, Acta Math. Hungar. 55 (1990).
J. Burzyk, A Paley‑Wiener type theorem for regular operators of bounded support, Studia Math. 93 (1989), 187‑200.
D. Nemzer, Periodic Boehmians, Internat. J. Math. Math. Sci. 12 (1989), 685-692.
J. Burzyk, Nonharmonic
solutions of the Laplace equation, in Generalized functions, convergence structures,
and their applications (
P. Mikusinski, On delta sequences, Rend. Istit.
Mat. Univ.
P. Mikusinski, On harmonic Boehmians, Proc. Amer. Math. Soc. 106 (1989), 447-449.
P. Mikusinski, A remark on regular operators, Rocky Mountain J. Math. 19 (1989, 429-432.
T. K. Boehme, Some comments on the Burzyk-Paley-Wiener
theorem for regular operators, in Generalized functions, convergence
structures, and their applications (
P. Mikusinski, Boehmians and generalized functions, Acta Math. Hungar. 51 (1988), 271-281.
P. Mikusinski, Fourier transform for integrable Boehmians,
R. Gedeon, Hilbert Transform of Generalized Functions, Ph.D. Thesis, University of California, Santa Barbara, 1986.
D. Nemzer, The Boehmians as an F-Space, Ph.D. Thesis, University of California, Santa Barbara, 1984.
J. Burzyk, On type II convergence in the Mikusinski operational calculus, Studia Math. 77 (1983), 17-27.
J. Burzyk, On convergence in the Mikusinski operational calculus, Studia Math. 75 (1983), 313-333.
P. Mikusinski, Convergence of
P. Mikusinski, Convergence dans l'ensemble des quotients de suites (French), [Convergence in the space of quotients of sequences], C. R. Acad. Sci. Paris Sér. I Math. 294 (1982), 87-89.
J. Mikusinski and P. Mikusinski, Quotients de suites et leurs applications dans l'analyse fonctionnelle (French), [Quotients of sequences and their applications in functional analysis], C. R. Acad. Sci. Paris Sér. I Math. 293 (1981), 463-464.
T. K. Boehme, The support of Mikusi\'nski operators, Trans. Amer. Math. Soc. 176 (1973), 319-334.