Asensio, V., Jornet, D.: Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113(4), 3477–3512 (2019)
Aubry, J.-M.: Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices. J. Lond. Math. Soc. 2(78), 392–406 (2008)
Björck, G.: Linear partial differential operators and generalized distributions. Ark. Mat. 6(21), 351–407 (1966)
[+]
Asensio, V., Jornet, D.: Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113(4), 3477–3512 (2019)
Aubry, J.-M.: Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices. J. Lond. Math. Soc. 2(78), 392–406 (2008)
Björck, G.: Linear partial differential operators and generalized distributions. Ark. Mat. 6(21), 351–407 (1966)
Bierstedt, K.D., Bonet, J.: Some aspects of the modern theory of Fréchet spaces. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 97(2), 159–188 (2003)
Bierstedt, K.D., Meise, R.: Distinguished echelon spaces and the projective description of weighted inductive limits of type $${\cal{V}} _{d}\cal{C} (X)$$. In: Aspects of Mathematics and Its Applications. North-Holland Mathematics Library, Amsterdam, vol. 34, pp. 169–226 (1986)
Boiti, C., Jornet, D., Oliaro, A.: Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms. J. Math. Anal. Appl. 446, 920–944 (2017)
Boiti, C., Jornet, D., Oliaro, A.: The Gabor wave front set in spaces of ultradifferentiable functions. Monatsh. Math. 188(2), 199–246 (2019)
Boiti, C., Jornet, D., Oliaro, A.: Real Paley-Wiener theorems in spaces of ultradifferentiable functions. J. Funct. Anal. 278(4), 108348 (2020)
Boiti, C., Jornet, D., Oliaro, A.: About the nuclearity of $$\cal{S}_{(M_{p})}$$ and $${\cal{S}}_{\omega }$$. In: Boggiatto P. et al. (eds) Advances in Microlocal and Time-Frequency Analysis. Applied and Numerical Harmonic Analysis, pp. 121–129. Birkhäuser, Cham (2020)
Boiti, C., Jornet, D., Oliaro, A., Schindl, G.: Nuclearity of rapidly decreasing ultradifferentiable functions and time-frequency analysis. Collect. Math. (2020). https://doi.org/10.1007/s13348-020-00296-0
Bonet, J., Meise, R., Melikhov, S.N.: A comparison of two different ways to define classes of ultradifferentiable functions. Bull. Belg. Math. Soc. Simon Stevin 14(3), 425–444 (2007)
Braun, R.W., Meise, R., Taylor, B.A.: Ultradifferentiable functions and Fourier analysis. Result. Math. 17, 206–237 (1990)
Cordero, E., Pilipović, S., Rodino, L., Teofanov, N.: Quasianalytic Gelfand-Shilov spaces with application to localization operators. Rocky Mt. J. Math. 40, 1123–1147 (2010)
Debrouwere, A., Neyt, L., Vindas, J.: Characterization of nuclearity for Beurling-Björck spaces. Preprint (2019). arXiv: 1908.10886
Debrouwere, A., Neyt, L., Vindas, J.: The nuclearity of Gelfand-Shilov spaces and kernel theorems. Collect. Math. (2020). https://doi.org/10.1007/s13348-020-00286-2
Fernández, C., Galbis, A., Jornet, D.: Pseudodifferential operators on non-quasianalytic classes of Beurling type. Stud. Math. 167(2), 99–131 (2005)
Fernández, C., Galbis, A., Jornet, D.: Pseudodifferential operators of Beurling type and the wave front set. J. Math. Anal. Appl. 340(2), 1153–1170 (2008)
Gel’fand, I.M., Shilov, G.E.: Generalized functions, vol. 2. In: Spaces of Fundamental and Generalized Functions. Translated from the Russian by Morris D. Friedman, Amiel Feinstein and Christian P. Peltzer. Academic Press (Harcourt Brace Jovanovich, Publishers), New York 1968 (1977)
Gel’fand, I.M., Vilenkin, N.Ya.: Generalized functions, vol. 4. In: Applications of Harmonic Analysis. Translated by Amiel Feinstein. Academic Press, New York (1964)
Grothendieck, A.: Produits tensoriels topologiques et espaces nucléaires. (French) Mem. Am. Math. Soc. 16 (1955)
Gröchenig, K.: Foundations of Time-Frequency Analysis. Birkhäuser, Boston (2001)
Gröchenig, K., Zimmermann, G.: Spaces of test functions via the STFT. J. Funct. Spaces Appl. 2(1), 25–53 (2004)
Hörmander, L.: A uniqueness theorem of Beurling for Fourier transform pairs. Ark. Mat. 29, 237–240 (1991)
Hörmander, L.: Notions of convexity. In: Progress in Mathematics, vol. 127. Birkhäuser Boston (1994)
Jiménez-Garrido, J., Sanz, J., Schindl, G.: Sectorial extensions, via Laplace transforms, in ultraholomorphic classes defined by weight functions. Result Math. 74(27) (2019)
Komatsu, H.: Ultradistributions I. Structure theorems and a characterization. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 20, 25–105 (1973)
Kruse, K.: On the nuclearity of weighted spaces of smooth functions. Ann. Polon. Math. 124(2), 173–196 (2020)
Langenbruch, M.: Hermite functions and weighted spaces of generalized functions. Manuscr. Math. 119(3), 269–285 (2006)
Lozanov-Crvenković, Z., Perišić, D.: Hermite expansions of elements of Gelfand-Shilov spaces in quasianalytic and non quasianalytic case. Novi Sad J. Math. 37, 129–147 (2007)
Mandelbrojt, S.: Sér. Adhér. Régularisation des suites, Applications, Gauthier-Villars, Paris (1952)
Mitjagin, B.S.: Nuclearity and other properties of spaces of type S. Trudy Moskov. Mat. Obsc. 9, 317–328 (1960)
Meise, R., Vogt, D.: Introduction to Functional Analysis. Clarendon Press, Oxford (1997)
Nicola, F., Rodino, L.: Global pseudo-differential calculus on Euclidean spaces. In: Pseudo-Differential Operators. Theory and Applications, vol. 4. Birkhäuser, Basel (2010)
Pietsch, A.: Nuclear Locally Convex Spaces. Springer, New York (1972)
Pilipović, S.: Tempered ultradistributions. Boll. Unione Mat. Ital., VII. Ser., B (7) 2(2), 235–251 (1988)
Pilipović, S.: Generalization of Zemanian spaces of generalized functions which have orthonormal series expansions. SIAM J. Math. Anal. 17, 477–484 (1986)
Rainer, A., Schindl, G.: Composition in ultradifferentiable classes. Stud. Math. 224(2), 97–131 (2014)
Rodino, L., Wahlberg, P.: The Gabor wave front set. Monatsh. Math. 173, 625–655 (2014)
Schindl, G.: Spaces of smooth functions of Denjoy-Carleman-type, 2009. Diploma Thesis, Universität Wien. http://othes.univie.ac.at/7715/1/2009-11-18_0304518.pdf
Schindl, G.: Exponential laws for classes of Denjoy-Carleman-differentiable mappings, 2014. PhD Thesis, Universität Wien. http://othes.univie.ac.at/32755/1/2014-01-26_0304518.pdf
Zhang, G.Z.: Theory of distributions of $$S$$ type and expansions. Chin. Math. 4, 211–221 (1963)
[-]
