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                                       FABRIZIO
COLOMBO
                                                                                SCIENTIFIC PUBBLICATIONS

1 F. Colombo, V. Vespri:
Generation of analytic semigroups in W^{k,p} and C^k,
Differential and Integral Equations,  6 (1996), 421-436.
2 F. Colombo:
Quasilinear Parabolic Equations in C^k  Spaces,
Dynamic Systems and Applications, 6 (1997),  271-296.
3 F. Colombo,  A. Lorenzi:
Identification of time and space dependent relaxation kernels in the theory of materials with memory I,
Journal of Mathematical Analysis and Applications,  213 (1997),  32-62.
4 F. Colombo, A. Lorenzi:
Identification of time and space dependent relaxation kernels in the theory of materials with memory II,
Journal of Mathematical Analysis and Applications,  213 (1997),  63-90.
5 F. Colombo,  A. Lorenzi:
An inverse problem in the theory of combustion of materials with memory,
Advances in Differential Equations,  3 (1998), 133-154.
6 F.Colombo, P. Loustaunau, I. Sabadini,  D.C. Struppa:
Regular functions of biquaternionic variables and Maxwell's equations,
Journal of Geometry and Physics,  26 (1998), 183-201.
7 F. Colombo: 
Problemi inversi, equazioni quasilineari e semigruppi analitici,
Estratto  della Tesi di Dottorato, Bollettino UMI, 1-A  (1998), 97-100.
8 F. Colombo,  M. Giuli, V. Vespri:
Generation of smoothing semigroups by degenerate elliptic operators arising in financial mathematics,
Communications in Applied Analysis,  3 (1999), 283-202.
9 F. Colombo,  R. Monte, V. Vespri:
On Some Equations About European Option Pricing,
Proceedings of the 18th IFIP Conference on Systems Modeling and Optimization,
(Detroit, MI, 1997) Addison Wesley Longman, Research notes in Mathematics,   396 (1999),  33-41.
10 F.Colombo,  I. Sabadini,  D.C. Struppa:
Dirac equation in the octonionic algebra,
Contemporary Mathematics AMS,   251 (2000), 117-134.
11 F. Colombo,  A. Lorenzi:
An identification problem related to a parabolic integrodifferential equation with non commuting spatial operators,
Journal Inverse and Ill-posed Problems,  8 (2000),  505-540.
12 F. Colombo:
Continuous dependence results for an inverse problem in the theory of combustion of materials with memory,
Rendiconti Istituto Matematico Universita` di Trieste,  32 (2000), 189-215.
13 F. Colombo:
A quasilinear parabolic inverse problem in Holder spaces,
Differential and Integral Equations,  14 (2001), 1237-1258.
14 F. Colombo:
Direct and inverse problems for a phase field model with memory,
Journal of Mathematical Analysis and Applications,  260 (2001),  517-545.
15 F. Colombo: 
Some inverse  problems related to the heat equation with memory in non smooth spatial domains,
Series on Advances in Mathematics for Applied Sciences: Mathematical Models and Methods for Smart Materials.
Editors M. Fabrizio, B. Lazzari, A. Morro,  62 (2002), 61-72.
16 F. Colombo D. Guidetti,  A. Lorenzi:
Elliptic equations in non-smooth plane domains with an application to a parabolic problem,
Advances in Differential Equations,  7 (2002), 695-716.
17 F. Colombo:
An inverse problem for a generalized Kermack-McKendrick model,
Journal of Inverse and Ill-Posed Problems, 10 (2002), 221-241.
18 C. Cavaterra,  F. Colombo:
Automatic control problems for reaction diffusion systems,
Journal of Evolution Equations,  2 (2002), 241-273.
19 F. Colombo, D. Guidetti:
A unified approach to nonlinear  integro-differential inverse problems of  parabolic type,
Zeitschrift fur Analysis und ihre Anwendungen, 21 (2002),  431-464.
20 F. Colombo I. Sabadini, F. Sommen,  D. C. Struppa:
Syzygies and conservation laws,
Foundations of Physics Letters,  15 (2002), 507-522.
21 F. Colombo,  M. Giuli, V. Vespri:
A Semigroup Approach to No-Arbitrage Pricing Theory: Constant Elasticity Variance Model and Term Structure Models,
Proceedings of ``Evolution Equation 2000: Appl. to Phys., Ind., Life Sci. Econ. EVEQ 2000'', (2002).
22 F. Colombo, V. Vespri:
A semilinear integrodifferential inverse problem,
Evolution equations, J. Goldstein, R. Nagel and S. Romanelli editors, Marcel Dekker, Inc.  (2003) , 91-104, cap.6.
23 F. Colombo, D. Guidetti,  A. Lorenzi:
On  applications of maximal regularity to inverse  problems for integrodifferential equations of parabolic type,
Evolution equations, J. Goldstein, R. Nagel and S. Romanelli editors, Marcel Dekker, Inc. 2003, 77-90,  cap.5.
24 F. Colombo,  I. Sabadini , D.C. Struppa:
An introduction to Computational Algebraic Analysis,
Milan Journal of  Mathematics, 71 (2003),  1-36.
25 F. Colombo,  D. Guidetti, A. Lorenzi:
Integrodifferential  identification problems for thermal materials with memory in non-smooth plane domains,
Dynamic Systems and Applications,  12  (2003),  533-560.
26 F. Colombo,  D. Guidetti,  A. Lorenzi:
Inegrodifferential identification problems for  the heat equation in cylindrical domains,
Advances in Mathematical Science and Application,  13 (2003), 639-662.
27 C. Cavaterra,  F. Colombo:
Identifying a heat source in automatic control problem,
Communication on Applied Nonlinear Analysis,  11 (2004), 1-23.
28 F. Colombo, F. Tomarelli:
Boundary value problems and obstacle problem for elastic bodies with free cracks ,
Calculus of Variations: Topics from the Mathematical Heritage of Ennio De Giorgi, D. Pallara (ed.),
Quaderni di Mathematica,  14. Series edited by Dipartimento di Matematica della Seconda Universita`
di Napoli, (2004).
29 F. Colombo,  A. Damiano,  I. Sabadini and  D.C. Struppa:
A surjectivity theorem for differential operators on spaces of regular functions,
Complex Variables Theory and Application,  50 (2005),  389-400.

30 F. Colombo and   D. Guidetti:
An inverse problem for a phase-field model in Sobolev spaces,
Nonlinear elliptic and parabolic problems,
189-210,
Progr. Nonlinear Differential Equations Appl., 64, Birkhäuser, Basel, 2005.
31 F. Colombo:
Quasilinear Systems with Memory Kernels,

Journal of Mathematical Analysis and Applications, 311 (2005), 40-68.

32 F. Colombo,  D. Guidetti, V. Vespri:
Identification of two memory kernels and the time dependence of the heat source for a parabolic conserved phase-field model,
Mathematical Methods for the Applied Science,  28 (2005), 2085-2115.
33 F. Colombo,  D. Guidetti,  A. Lorenzi,  V. Vespri:
Some recent results on  inverse problems  arising from phase-field models,
RIMS Kokyuroku,  1436 (2005), 66-87.
34 F. Colombo,  V. Soucek,  D. C. Struppa:
 Invariant resolutions for several Fueter operators,
Journal of Geometry and Physics,  56 (2006),  1175- 1191.
35 Colombo, D. Guidetti, V. Vespri :
A global in time result for an integro-differential parabolic inverse problem in the space of bounded functions,
Dissipative phase transitions,  65--86, Ser. Adv. Math. Appl. Sci., 71, World Sci. Publ., Hackensack, NJ, 2006.
36 F. Colombo, D. Guidetti , V. Vespri :
Some  global in time results  for integro-differential  parabolic inverse  problems,
Differential equations: inverse and direct problems, 35-58,
Lect. Notes Pure Appl. Math., 251, Chapman & Hall/CRC, Boca Raton, FL, 2006.
37 F. Colombo, A. Damiano:
Identification of the memory kernel and the heat source for a phase-field model,

Houston Journal of Mathematics,  32 (2006),  895-920.
38 F. Colombo,  D. Guidetti :
A global in time existence and uniqueness result for a semilinear integrodifferential parabolic  inverse problem in Sobolev Spaces,
Mathematical Models and Methods in Applied Science, 17 (2007), 1-29.
39 F. Colombo:
An inverse problem for the strongly damped wave equation with memory,
Nonlinearity, 20 (2007), 659-683.

40 F. Colombo, M.E Luna-Elizarraras, I. Sabadini, M.V. Shapiro,   D.C. Struppa:
A new characterization of pseudoconvex domains in C^2,
Comptes Rendus Math. Acad. Sci. Paris,  334 (2007),  677-680.
41 F. Colombo,  A. Damiano, I. Sabadini,  D.C. Struppa:
Quaternionic hyperfunctions on 5-dimensional varieties in H^2,
Journal of  Geometrical Analysis,  17 (2007), 459-478.
42 F. Colombo, G. Gentili, I. Sabadini,  D.C. Struppa:
A functional calculus in a non commutative  setting,
Electronic Research Announcements in Mathematical Sciences,  14 (2007),  60-68.
43 F. Colombo:
An inverse problem  for a parabolic integrodifferential model in the theory of combustion,
Physica D, 236 (2007),  81-89.

44 F. Colombo, I. Sabadini, D.C. Struppa:
A new functional calculus for non commuting operators,
Journal of Functional Analysis,  254 (2008),  2255-2274.
45 F. Colombo,  D. Guidetti:
An inverse problem for the beam equation with memory with non homogeneous boundary conditions,
Inverse Problems,  24 (2008),  065015 (28p).
46 F. Colombo, G. Gentili, I. Sabadini,  D.C. Struppa:
An overview on functional calculi in different settings,
Hypercomplex Analysis, Trends in Mathematics, Birkhauser, 69-99, 2009.
47 F. Colombo, I. Sabadini:
A structure formula for  slice monogenic functions and some of its consequences,
Hypercomplex Analysis, Trends in Mathematics, Birkhauser, 101-114,  2009.
48 F. Colombo,  D. Guidetti: 
Identification of the memory  kernel in the strongly damped wave equation by a flux condition,
Communication on Pure and Applied Analysis,  8 (2009), 601-620.
49 F. Colombo, I. Sabadini:
On some properties of the quaternionic functional calculus,
Journal of  Geometric Analysis, 19 (2009), 601-627.
50 F. Colombo:
Global in time results for a class of inverse problems,
Journal of Inverse and Ill-Posed Problems, 17 (2009), 259-287.
51 F. Colombo,  I. Sabadini, D.C. Struppa:
Slice monogenic functions,
Israel Journal of Mathematics, 171  (2009), 385-403.
52 F. Colombo,  A. Damiano, I. Sabadini, D. C. Struppa:
A new Dolbeault complex in quaternionic and Clifford analysis,
More Progresses in Analysis, Proceedings of the 5th ISAAC Conference, 1019-1032.
53 F. Colombo,  A. Damiano, I. Sabadini, D. C. Struppa:
A functional calculus for n-tuples of non-commuting operators,
Advances in Applied Clifford Algebra,  19 (2009),  225-236.
54 F. Colombo,  I. Sabadini, D.C. Struppa, A. Vajiac, M. Vajiac:
Computational algebra techniques in electromagnetism,
Journal of mathematical science: advances and applications, 3 (2009), 77-88.
55 F. Colombo, G. Gentili, I. Sabadini, D. C. Struppa:
Extension results for slice regular functions of a quaternionic variable,
Advances in Mathematics,  222 (2009),  1793-1808.
56 F. Colombo,  D. Guidetti:
Some results on the reconstruction of  a convolution kernel in an integrodifferential  beam equation,
Communication to SIMAI Congress,  3 (2009), 264 (10p).
57 F. Colombo:
Stability and global in time  results for an inverse problem related to a nuclear reactor model,
Inverse Problems, 25 (2009), 105007 (20p).
58 F. Colombo,  G. Gentili, I. Sabadini, D.C. Struppa:
Non commutative functional calculus:  unbounded operators,
Journal of Geometry and Physics,  60 (2010), 251-259.
59 F. Colombo,  G. Gentili, I. Sabadini, D.C. Struppa:
Non commutative functional calculus:  bounded operators,
Complex Analysis and Operator Theory,  4  (2010), 821-843.
60 F. Colombo,  I. Sabadini, D.C. Struppa:
An extension theorem for slice monogenic functions and some of its consequences,
Israel Journal of Mathematics,  177 (2010), 369-389.
61 F. Colombo,  I. Sabadini, F. Sommen:
The Fueter mapping theorem in integral form and  the F-functional calculus,
Mathematical Methods in the Applied Science,  33 (2010), 2050-2066.
62 F. Colombo,  I. Sabadini, D.C. Struppa:
Duality theorems for slice hyperholomorphic functions,  
Journal fur die Reine und Angewandte Mathematik (Crelle's  Journal),  645 (2010), 85-104.
63 F. Colombo,   G. Gentili, I. Sabadini:
A Cauchy kernel for slice regular functions,
Annals of Global Analysis and Geometry,  37 (2010), 361-378.
64 F. Colombo:
An inverse problem for a linearized model in the theory of combustion,
Journal of Inverse and Ill-Posed Problems,  18 (2010), 167-187.
65 F. Colombo, I. Sabadini:
On the  formulations of the quaternionic functional calculus,
Journal of Geometry and Physics,  60 (2010), 1490-1508.
66 F. Colombo,  I. Sabadini, D.C. Struppa:
The Pompeiu formula for slice hyperholomorphic functions,

Michigan Mathematical Journal,  60 (2011), 163-170.
67 F. Colombo, I. Sabadini, D.C. Struppa, A. Vajiac, M. Vajiac:
Singularities of functions of one and several bicomplex variables,
Arkiv for Matematik (Institute Mittag-Leffler),  49 (2011), 277-294.
68 F. Colombo, I. Sabadini:
Bounded perturbations of the resolvent operators associated to the  F-spectrum,
Hypercomplex Analysis and Applications, Trends in Mathematics, Birkhauser, (2011), 13-28.
69 F. Colombo, I. Sabadini,  D.C. Struppa, A. Vajiac, M. Vajiac:
Bicomplex hyperfunctions,
Annali di Matematica Pura ed Applicata,  190 (2011), 247-261.
70  F. Colombo, I. Sabadini:
The Cauchy formula with s-monogenic kernel and a functional calculus for noncommuting operators,
Journal of Mathematical Analysis and Applications,  373 (2011), 655-679.
71 F. Colombo, I. Sabadini:
The quaternionic evolution operator,
Advances in Mathematics,  227 (2011), 1772-1805.
72 F. Colombo, D. Guidetti:
Some results on the identification of memory kernels,
in Modern Aspects of the Theory of Partial Differential Equations, Series: Operator Theory: Advances and Applications,
Vol. 216, p.121-138, Ruzhansky, Michael; Wirth, Jens (Eds.) 1st Edition,  (2011).
73 F. Colombo, I. Sabadini,  D.C. Struppa:
The Runge theorem for slice hyperholomorphic functions,
Proceedings American Mathematical Society,  139  (2011), 1787-1803.
74 F. Colombo, J. O. Gonzalez-Cervantes, I. Sabadini:
Comparison of the Various Notions of Slice Monogenic Functions and their Variations,
 Conf. Proc. ICNAAM,  1389  (2011), 264--267, Vol. A, B and C, American Institute of Physics.
75 F. Colombo, I. Sabadini, F. Sommen:
The inverse Fueter mapping theorem,
Communication on Pure and Applied Analysis, 10 (2011), 1165-1181.
76 F. Colombo, Y. Aharonov,  I. Sabadini, D.C. Struppa, J. Tollaksen:
Some mathematical properties of  superoscillations,
Journal of Physics A: Mathematical and  Theoretical,   44 (2011), 365304 (16pp). 
77 F. Colombo, J. O. Gonzalez-Cervantes, I. Sabadini:
The Bergman-Sce transform for slice monogenic functions,
Mathematical Methods in the Applied Sciences,  34 (2011), 1896- 1909.
78 F. Colombo, I. Sabadini:
The  F-spectrum and the SC-functional calculus,
Proceedings of the Royal Society of Edinburgh, Section A, 142  (2012), 479-500.            
79 F. Colombo,  M. E. Luna-Elizarraras, I. Sabadini, M. Shapiro, D.C. Struppa:
A quaternionic treatment of the inhomogeneous div-rot system,
Moscow Mathematical Journal,  12 (2012), 37-48.
80 F. Colombo, M.E. Luna-Elizarraras,  I. Sabadini, M.V. Shapiro , D.C. Struppa:
Integral conditions for the vanishing of cohomology of open sets in C^n,
Advances in Geometry,  12  (2012), 191--201.
81 F. Colombo, J. O. Gonzalez-Cervantes, I. Sabadini,
On slice biregular functions and isomorphisms of Bergman spaces,
Complex Variables and Elliptic Equations,   57  (2012),  825-839.
82 F. Colombo, I. Sabadini:
An invitation to the S-functional calculus,
in Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations
Operator Theory: Advances and Applications,  221 (2012), 241-254.
83 D. Alpay, F. Colombo, I. Sabadini:
Schur functions and their realizations in the slice hyperholomorphic setting,
Integral Equations and Operator Theory,  72 (2012), 253-289.
84 F. Colombo,  I. Sabadini, D.C. Struppa:
Duality theorems in the Hermitian setting,

Journal of Mathematical Analysis and its Applications, 390 (2012), 47-58.
85 F. Colombo, I. Sabadini:
On some notions of spectra for quaternionic operators and for n-tuples of operators,

C. R. Acad. Sci. Paris, Ser. I, 350 (2012), 399-402.
86 F. Colombo, I. Sabadini, F. Sommen:
An overview on the Inverse Fueter Mapping Theorem,
Amer. Inst. Phys.  Conf. Proc.: AIP Conf. Proc. 1479, 279 (2012).
87 D. Alpay, F. Colombo, I. Sabadini:
Schur analysis in the slice hypercomplex setting,
Amer. Inst. Phys.  Conf. Proc.:  AIP Conf. Proc. 1479, 325 (2012).
88 F. Colombo, I. Sabadini, D. C. Struppa:
Sheaves of  slice regular functions,
Mathematische Nachrichten,  285 (2012), 949-958.
89 Y. Aharonov, F. Colombo,  I. Sabadini, S. Nussinov, D.C. Struppa, J. Tollaksen:
 Superoscillations phenomenona in SO(3),
Proceedings of the Royal Society A: Mathematical, Physical, 468 (2012), 3587-3600.
90 F. Colombo, I. Sabadini:
Some remarks on the  S-spectrum,
Complex Variables and Elliptic Equations, 58 (2013), 1--6.
91 F. Colombo, J. O. Gonzalez-Cervantes,   I. Sabadini:
A non constant coefficients differential operator associated to slice monogenic functions,
Transactions of the American Mathematical Society,  365 (2013), 303-318.
92 F. Colombo, J. O. Gonzalez-Cervantes,   I. Sabadini:
The C-property for slice regular functions and applications to the Bergman space,
 Complex Variables and Elliptic Equations,  (2013).
93 F. Colombo, I. Sabadini, F. Sommen:
The inverse Fueter mapping theorem in integral form using spherical monogenics, 
Israel Journal of Mathematics (2013)
94 Y. Aharonov, F. Colombo,  I. Sabadini, D.C. Struppa, J. Tollaksen:
On some operators associated to   superoscillations,

Complex Analysis and Operator Theory, (2013).
95 Y. Aharonov, F. Colombo,  I. Sabadini, D.C. Struppa, J. Tollaksen:
On the Cauchy problem for the Schrodinger equation with superoscillatory initial data,
Journal Mathematiques Pures Appliquees, 99 (2013), 165--173.
96 F. Colombo, J. O. Gonzalez-Cervantes, M.E. Luna-Elizarraras,  I. Sabadini, M.V. Shapiro:
On two approaches to the Bergman theory for slice regular functions,
Advances in Hypercomplex Analysis; Springer INdAM Series 1, (2013), 39--54.
97 F. Colombo, I. Sabadini,  D. C. Struppa:
Algebraic properties of the module of slice regular functions in several quaternionic variables,
Indiana University Mathematics Journal, (2013).
98 D. Alpay, F. Colombo, I. Sabadini:
Pontryagin  De Branges Rovnyak spaces of slice hyperholomorphic functions,

Journal d'Analyse Mathematique, (2013).
99 D. Alpay, F. Colombo, I. Sabadini:
Krein-Langer factorization and related topics in the slice hyperholomorphic setting,
Journal of  Geometric Analysis, (2013).
100 F. Colombo,  J. O. Gonzalez-Cervantes, I. Sabadini:
Some integral representations for slice hyperholomorphic functions,
submitted.
101 F. Colombo, I. Sabadini, F. Sommen,:
The Fueter  primitive of biaxially monogenic functions,
submitted.
102 F. Colombo, I. Sabadini, F. Sommen,  D. C. Struppa:
Twisted plane wave expansions using hypercomplex methods,
submitted.
103 F. Colombo, I. Sabadini,  D. C. Struppa:
Bicomplex holomorphic functional calculus,
submitted.
104 Y. Aharonov, F. Colombo, I. Sabadini, D.C. Struppa, J. Tollaksen:
On superoscillations longevity: a windowed Fourier transform approach,
submitted.
105 D. Alpay, V. Bolotnikov, F. Colombo,  I. Sabadini:
Inner product spaces and Krein spaces in the quaternionic setting,
preprinit.
106 Y. Aharonov, F. Colombo,  I. Sabadini, D.C. Struppa, J. Tollaksen:
Superoscillating sequences as solutions of  generalized Schrodinger equations,
submitted.
107 F. Colombo,  D. Pena Pena,  I. Sabadini, F. Sommen
A new integral formula for the inverse Fueter mapping theorem,
submitted.