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Applicable Analysis
An International Journal
Volume 16, 1983 - Issue 1
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Original Articles

The weierstrass transform and an isometry in the heat equation

S. Saitoh Department of Mathematics, Gunma University, Tenjin-cho, Kiryu, 376, Japan
Pages 1-6 | Received 20 Sep 1982, Published online: 02 May 2007

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Moncef Dziri & Anis Kroumi. (2023) Tikhonov regularisation for the Weierstrass transform associated with the Kontorovich–Lebedev transform. Complex Variables and Elliptic Equations 68:7, pages 1119-1131.
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Nemri Akram. (2022) On a q-best approximation formulas for the L2-multiplier operators and applications. Research in Mathematics 9:1.
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Lakhdar T. Rachdi & Samia Sghaier. (2019) The windowed Fourier transform and Gabor multipliers associated with the Riemann-Liouvlle transform. Integral Transforms and Special Functions 30:7, pages 564-580.
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Fethi Soltani & Akram Nemri. (2015) Analytical and numerical applications for the Fourier multiplier operators on ℝ × (0, ∞). Applicable Analysis 94:8, pages 1545-1560.
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Fethi Soltani. (2015) Inversion formulas for the Dunkl-type Segal–Bargmann transform. Integral Transforms and Special Functions 26:5, pages 325-339.
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Fethi Soltani. (2014) Dunkl multiplier operators and applications. Integral Transforms and Special Functions 25:11, pages 898-908.
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Fethi Soltani. (2014) Operators and Tikhonov regularization on the Fock space. Integral Transforms and Special Functions 25:4, pages 283-294.
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Fethi Soltani. (2013) Extremal functions on Sobolev–Dunkl spaces. Integral Transforms and Special Functions 24:7, pages 582-595.
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L.P. Castro & S. Saitoh. (2012) Natural outputs and global inputs of linear systems with a finite number of input data. Applicable Analysis 91:2, pages 225-236.
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L.P. Castro, Q. Chen & S. Saitoh. (2010) Source inversion of heat conduction from a finite number of observation data. Applicable Analysis 89:6, pages 801-813.
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T. Matsuura & S. Saitoh. (2006) Analytical and numerical inversion formulas in the Gaussian convolution by using the Paley–Wiener spaces. Applicable Analysis 85:8, pages 901-915.
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Fethi Soltani . (2005) Practical inversion formulas in a quantum mechanical system. Applicable Analysis 84:8, pages 759-767.
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Fethi Soltani. (2005) Inversion formulas in the Dunkl-type heat conduction on . Applicable Analysis 84:6, pages 541-553.
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S. Saitoh. (2004) Approximate real inversion formulas of the gaussian convolution. Applicable Analysis 83:7, pages 727-733.
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Saburou Saitoh. (1995) One approach to some general integral transforms and its applications. Integral Transforms and Special Functions 3:1, pages 49-84.
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Du-Won Byun & Saburou Saitoh. (1995) Analytic extensions of functions on the real line to entire functions . Complex Variables, Theory and Application: An International Journal 26:4, pages 277-281.
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S. Saitoh. (1991) Isometrical identities and inverse formulas in the one-dimensional heat equation. Applicable Analysis 40:2-3, pages 139-149.
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Saburou Saitoh. (1990) Isometrical identities and iverse formulas in the one-dimensional schrödinger equation. Complex Variables, Theory and Application: An International Journal 15:2, pages 135-148.
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Saburou Saitoh. (1984) Integral transforms in linear equations of parabolic type with constant coefficients. Applicable Analysis 18:1-2, pages 13-27.
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Fethi Soltani & Meriem Nenni. (2023) DIFFERENCE AND PRIMITIVE OPERATORS ON THE DUNKL-TYPE FOCK SPACE $$\mathscr {F}_{\alpha }(\mathbb {C}^{d})$$. Journal of Mathematical Sciences 266:6, pages 917-932.
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Hari M. Srivastava, Abhishek Singh, Aparna Rawat & Shubha Singh. (2021) A family of Mexican hat wavelet transforms associated with an isometry in the heat equation. Mathematical Methods in the Applied Sciences 44:14, pages 11340-11349.
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Firdous A. Shah, Kottakkaran S. Nisar, Waseem Z. Lone & Azhar Y. Tantary. (2021) Uncertainty principles for the quadratic‐phase Fourier transforms. Mathematical Methods in the Applied Sciences 44:13, pages 10416-10431.
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Fethi Soltani. (2015) Some Examples of Extremal Functions on the Dunkl-Type Fock Space $$F_k(\mathbb {C})$$ F k ( C ). Complex Analysis and Operator Theory 10:7, pages 1501-1517.
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Norazrizal Rahman & Muhammad Ahmad. (2015) Applications of the Fuzzy Sumudu Transform for the Solution of First Order Fuzzy Differential Equations. Entropy 17:12, pages 4582-4601.
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Fethi Soltani & Akram Nemri. (2014) Analytical and Numerical Approximation Formulas for the Fourier Multiplier Operators. Complex Analysis and Operator Theory 9:1, pages 121-138.
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Fethi Soltani. (2014) Uncertainty Principles and Extremal Functions for the Dunkl -Multiplier Operators . Journal of Operators 2014, pages 1-9.
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Mourad Jelassi & Hatem Mejjaoli. (2014) Sobolev-Type Spaces on the Dual of the Chébli-Trimèche Hypergroup and Applications. Abstract and Applied Analysis 2014, pages 1-13.
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Fethi Soltani. (2013) Extremal Functions on Sturm–Liouville Hypergroups. Complex Analysis and Operator Theory 8:1, pages 311-325.
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Chelo Ferreira & Jos? L. L?pez. (2012) Approximations of the Poisson transform for large and small values of the transformation parameter. The Ramanujan Journal 30:3, pages 309-326.
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Hassen Ben Mohamed & Belgacem Ghribi. (2012) Weinstein-Sobolev spaces of exponential type and applications. Acta Mathematica Sinica, English Series 29:3, pages 591-608.
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L.T. Rachdi & N. Msehli. (2012) Best approximation for weierstrass transform connected with spherical mean operator. Acta Mathematica Scientia 32:2, pages 455-470.
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Nguyen Minh Tuan & Nguyen Thi Thu Huyen. (2010) The Hermite Functions Related to Infinite Series of Generalized Convolutions and Applications. Complex Analysis and Operator Theory 6:1, pages 219-236.
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Saburou Saitoh. (2007) Applications of Tikhonov regularization to inverse problems using reproducing kernels. Journal of Physics: Conference Series 73, pages 012019.
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T. Matsuura, S. Saitoh & D. D. Trong. (2005) Approximate and analytical inversion formulas in heat conduction on multidimensional spaces. Journal of Inverse and Ill-posed Problems 13:5, pages 479-493.
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Andrzej Borowiec, Jerzy Lukierski, Vladimir Lyakhovsky, Marek Mozrzymas & Valeriy N. Tolstoy. (2005) Basic twist quantization of the exceptional Lie algebra g2. Journal of Mathematical Physics 46:10.
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Saburou Saitoh. 2003. Analysis and Applications — ISAAC 2001. Analysis and Applications — ISAAC 2001 135 150 .
Saburou Saitoh. 2001. Analytic Extension Formulas and their Applications. Analytic Extension Formulas and their Applications 207 232 .
Gen Nakamura, Sabrou Saitoh & Admi Syarif. 2001. Proceedings of the Second ISAAC Congress. Proceedings of the Second ISAAC Congress 643 649 .
G Nakamura, S Saitoh & A Syarif. (1999) Representations of initial heat distributions by means of their heat distributions as functions of time. Inverse Problems 15:5, pages 1255-1261.
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Saburou Saitoh. 1999. Reproducing Kernels and their Applications. Reproducing Kernels and their Applications 165 188 .
Miki Tsuji. 2000. Recent Developments in Complex Analysis and Computer Algebra. Recent Developments in Complex Analysis and Computer Algebra 311 322 .
Saburou Saitoh. 1992. General Inequalities 6. General Inequalities 6 351 359 .

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