| Concrete construction by Fourier multipliers | statement | proposition 5.4 | arxiv |
| $\Op L=(-\Delta)^{\gamma/2}$ on $\Spc S(\R^d)$ | example | example 6.1 | arxiv |
| Characterization of spline admissibility | statement | theorem 5.1 | arxiv |
| Extension of $\Op L$ and uniqueness of the native space | statement | proposition 5.9 | arxiv |
| $\V p$-conditional Riesz pairs generated by $\Op L$ | statement | theorem 4.4 | arxiv |
| $\Lop$-compatible measurements | definition | definition 4.2 | arxiv |
| Characterization of $L_2$-realizable conditional pairs | statement | theorem 5.1 | arxiv |
| Hilbert--Gelfand space | definition | definition 2.2 | arxiv |
| Attainable null space | definition | definition 3.1 | arxiv |
| Attainable null space | definition | definition 3.1 | arxiv |
| Factorization of the conditional inverse | statement | proposition 5.5 | arxiv |
| Minimum-norm fitting in Hilbert space and Lagrange duality | statement | theorem 4.1 | arxiv |
| Conditioned factorization through a Green inverse of $\Op L^\ast$ | statement | corollary 5.7 | arxiv |
| Regular operator | definition | definition 5.2 | arxiv |
| Nuclear Gelfand pair | definition | definition 2.1 | arxiv |
| Compatible Riesz pair | definition | definition 2.4 | arxiv |
| Green inverse of the normal operator | statement | corollary 4.1 | arxiv |
| $\Op L=P(\Op D)$ on $\Spc S(\R)$ | example | example 6.3 | arxiv |
| Hilbert--Gelfand spaces and compatible Riesz pairs | statement | theorem 2.5 | arxiv |
| Positive-definite operator | definition | definition 2.3 | arxiv |
| $\V p$-conditional Riesz pair | definition | definition 3.2 | arxiv |
| Conditional positivity | definition | definition 5 | arxiv |
| Riesz representation criterion | statement | lemma 4.2 | arxiv |
| $\Op B=\Op D^\ast\Op D$ on $\Spc S(\R)$ | example | example 3.10 | arxiv |
| Sharpness for regular operators | statement | corollary 5.3 | arxiv |
| Augmented pair and direct-sum structure | statement | theorem 3.7 | arxiv |
| Realization | statement | proposition 3.3 | arxiv |
| $L_2$-realization of the conditional pair | statement | corollary 4.7 | arxiv |
| Attainable null space, conditional invertibility, and minimality | statement | theorem 3.4 | arxiv |
| $\V p$-conditional Riesz pair | definition | definition 3.2 | arxiv |
| Spline-admissible operator | definition | definition 2.6 | arxiv |
| Range of the conditional inverse | statement | proposition 3.2 | arxiv |
| Finite-dimensional Hilbert subspaces of $\Spc S'$ | statement | proposition 2.2 | arxiv |
| Nuclear Gelfand pair | definition | definition 2.1 | arxiv |
| Representer theorem for generalized variational splines | statement | theorem 4.3 | arxiv |
| Direct-sum decomposition of the measurement space | statement | lemma 4.4 | arxiv |
| Concretization | statement | theorem 3.6 | arxiv |
| Native space associated with an admissible operator $\Lop$ | statement | theorem 3.1 | arxiv |
| Algebraic characterization of compatibility | statement | corollary 2.6 | arxiv |
| Biorthogonal systems and projectors | statement | lemma 3.5 | arxiv |
| Independence from the biorthogonal family | statement | corollary 3.8 | arxiv |
