We consider pseudoquotient extensions of positive linear functionals on a commutative Banach algebra $\mathcal{A}$ and give conditions under which the constructed space of pseudoquotients can be identified with all Radon measures on the structure space $\hat{\mathcal{A}}$.
References
D. Atanasiu and P. Mikusiński,The Fourier transform of Levy measures on a semigroup, Integral Transform. Spec. Funct. 19 (2008), 537–543. MR2449620 10.1080/10652460802091500 D. Atanasiu and P. Mikusiński,The Fourier transform of Levy measures on a semigroup, Integral Transform. Spec. Funct. 19 (2008), 537–543. MR2449620 10.1080/10652460802091500
D. Atanasiu and P. Mikusiński, Fourier transform of Radon measures on locally compact groups, Integral Transform. Spec. Funct. 21 (2010), 815–821. MR2739390 10.1080/10652461003687781 D. Atanasiu and P. Mikusiński, Fourier transform of Radon measures on locally compact groups, Integral Transform. Spec. Funct. 21 (2010), 815–821. MR2739390 10.1080/10652461003687781
D. Atanasiu, P. Mikusiński, and D. Nemzer, An algebraic approach to tempered distributions, J. Math. Anal. Appl. 384 (2011), 307–319. MR2825185 10.1016/j.jmaa.2011.05.064 D. Atanasiu, P. Mikusiński, and D. Nemzer, An algebraic approach to tempered distributions, J. Math. Anal. Appl. 384 (2011), 307–319. MR2825185 10.1016/j.jmaa.2011.05.064
P. Mikusiński, Generalized quotients with applications in analysis, Methods Appl. Anal. 10 (2003), 377–386. MR2059942 10.4310/MAA.2003.v10.n3.a4 euclid.maa/1087841035
P. Mikusiński, Generalized quotients with applications in analysis, Methods Appl. Anal. 10 (2003), 377–386. MR2059942 10.4310/MAA.2003.v10.n3.a4 euclid.maa/1087841035