Introduction .................................................... 1
Chapter 1. Operator algebras associated with noncommutative
domains .............................................. 9
1.1. The noncommutative domain  ƒ and a universal model ......... 9
1.2. The domain algebra  n(ƒ) and its representations ......... 17
1.3. The Hardy algebra Fn∞(ƒ) .................................. 22
1.4. Functional calculus for n-tuples of operators in ƒ ....... 26
1.5. The noncommutative variety  ƒj and a functional
calculus .................................................. 32
1.6. Weighted shifts, symmetric weighted Fock spaces, and
multipliers ............................................... 35
Chapter 2. Free holomorphic functions on noncommutative
domains ............................................. 45
2.1. Free holomorphic functions and Poisson transforms ......... 45
2.2. Schwarz lemma and Bohr's inequality for Fn∞(ƒ) ............ 51
2.3. Weierstrass and Montel theorems for the algebra Hol(ƒ) ... 56
2.4. Cauchy transforms and analytic functional calculus for
n-tuples of operators ..................................... 59
Chapter 3. Model theory and unitary invariants on
noncommutative domains .............................. 71
3.1. Weighted shifts and invariant subspaces ................... 71
3.2. C*-algebras associated with noncommutative varieties
and Wold decompositions ................................... 76
3.3. Dilations on noncommutative domains and varieties ......... 82
3.4. Characteristic functions and model theory ................. 92
3.5. Curvature invariant for n-tuples of operators in p ...... 104
Chapter 4. Commutant lifting and applications ................. 111
4.1. Interpolation on noncommutative domains .................. 111
4.2. Corona theorem for a class of Hardy algebras ............. 117
4.1. Bibliography ............................................. 121
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